CN116029108A - Mechanical fault prediction method - Google Patents
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Abstract
The invention relates to the technical field of mechanical fault prediction, in particular to a mechanical fault prediction method. Comprising the following steps: s1, forming data to be predicted into a group of time sequences; s2, decomposing the time sequence into an eigenmode function and a residual sequence of a group of single component signals; s3, carrying out stability test on the eigen-mode function and the residual sequence of the single component signal, if not, carrying out operation of the step S4, and if so, jumping to operation of the step S5; s4, carrying out differential operation on the non-stationary sequence, establishing an ARIMA model, and jumping to the step S3 for operation; s5, judging ARIMA model parameters; s6, carrying out residual error detection on the residual error; s7, carrying out EMD reconstruction on the prediction sequences of all single component signals to obtain a prediction total value; and S8, comparing the machine data in the predicted total value with a set fault threshold value to obtain the residual life of the machine. The invention can complete prediction by only a small amount of data samples, has simple model, and only needs endogenous variables without other exogenous variables.
Description
Technical Field
The invention relates to the technical field of mechanical fault prediction, in particular to a mechanical fault prediction method.
Background
There are two main types of predictions for mechanical failure at present: based on the physical model, based on the data-driven type.
The method based on the physical model is characterized in that firstly, a model of a predicted object is simulated through dynamic modeling, and then, prediction is carried out according to the model, and the accuracy of the method is high. But has the disadvantage that it is difficult to build a physical model for a system in a complex environment. And different systems need to build different physical models, so that the universality is not strong.
The prediction based on data driving is to build a prediction model according to the collected historical data of the equipment, and a complex physical model is not required to be built, so that the mechanism of the system is not required to be known, and only sufficient data is needed. But has the disadvantage of requiring a large amount of historical data as support. If the applied system cannot collect enough historical data, prediction cannot be performed or prediction accuracy is extremely low.
Disclosure of Invention
In view of the above-mentioned drawbacks of the prior art, an object of the present invention is to provide a mechanical failure prediction method, which solves the problems that in the prior art, it is difficult to build a physical model for a system in a complex environment, a large amount of data is required for prediction based on data driving, and prediction accuracy is low.
To achieve the above and other related objects, the present invention provides a mechanical failure prediction method, including:
s1, selecting data to be predicted, and forming the data to be predicted into a group of time sequences x (t);
s2, decomposing the time series into a group of eigenmode functions imf of the single component signals by adopting empirical mode decomposition i (t) and residual sequence r 0 (t)；
S3, eigenmode function imf of the single component signal i (t) and residual sequence r 0 (t) performing a smoothness test, if the smoothness test is not passed, performing the steps ofS4, if the stability test is passed, the operation is skipped to the operation of the step S5;
s4, carrying out differential operation on the non-stationary sequence, establishing an ARIMA model, and jumping to the step S3 for operation;
s5, judging ARIMA model parameters through AIC criteria or BIC criteria;
s6, residual error detection is carried out on the residual error, and if the detection is passed, mechanical fault prediction is carried out;
s7, carrying out EMD reconstruction on the prediction sequences of all the single component signals to obtain a prediction total value;
and S8, comparing the mechanical data in the predicted total value with a set fault threshold value to obtain the residual life of the machine.
In an embodiment of the present invention, the data to be predicted in step S1 is selected from an offline database or MySQL database.
In one embodiment of the present invention, the empirical mode decomposition is used in step S2 to decompose the time series into eigenmode functions imf of a set of single component signals i (t) and residual sequence r 0 (t) comprises:
obtaining local maximum values and limit values of the time sequence x (t), and constructing formulas of an upper envelope line h (t), a lower envelope line l (t) and an average value m (t) of the upper envelope line and the lower envelope line by using a cubic spline difference method, wherein the formulas are as follows:
r (t) is the difference between the time sequence x (t) and the mean value m (t) of the upper envelope and the lower envelope, whether r (t) is monotonous is judged, if so, an IMF sequence is decomposed, and the formula for obtaining a plurality of IMF sequences is as follows:
therein, imf i (t) is the ith IMF sequence obtained by empirical mode decomposition, r n (t) is a residual component of the signal after decomposing the n IMF sequences.
In an embodiment of the present invention, in step S3, if the smoothness test is not passed, the time sequence is a non-smooth sequence, and if the smoothness test is passed, the time sequence is a smooth sequence.
In an embodiment of the present invention, the ARIMA model in step S4 includes ARIMA model parameters d, d being the difference times.
In one embodiment of the present invention, the determining the ARIMA model parameters by AIC criteria in step S5 includes:
the ARIMA model parameter formula is judged by AIC criterion:
aic=2k-2 ln (L), where L is the likelihood function and k is the model complexity.
In one embodiment of the present invention, the determining the ARIMA model parameters according to the BIC criterion in step S5 includes:
selecting BIC minimum parameters to obtain p parameters and q parameters:
BIC(p,q)＝minBIC(p,q)。
in an embodiment of the present invention, the residual in step S6 is the time sequence subtracted by ARIMA model parameters including the number of differences d, the parameter p, and the parameter q.
As described above, the mechanical failure prediction method of the invention has the following beneficial effects:
the mechanical fault prediction method of the invention regards the time-varying data as a group of time sequences, can complete the prediction by only a small number of data samples, has simple model, and only needs endogenous variables without the help of other exogenous variables.
The mechanical failure prediction method reduces the dependence on the data quantity, has higher accuracy, and is suitable for application scenes with smaller data quantity.
The mechanical fault prediction method adopts two modes of an offline database and MySQL in the aspect of data management, and is convenient for users to select.
Drawings
Fig. 1 is a flowchart of a mechanical failure prediction method according to an embodiment of the present application.
Fig. 2 is a flowchart of a mechanical failure prediction method according to another embodiment of the present application.
Fig. 3 is a workflow diagram of EMD reconstruction of a mechanical failure prediction method according to an embodiment of the present application.
Detailed Description
Other advantages and effects of the present invention will become apparent to those skilled in the art from the following disclosure, which describes the embodiments of the present invention with reference to specific examples. The invention may be practiced or carried out in other embodiments that depart from the specific details, and the details of the present description may be modified or varied from the spirit and scope of the present invention. It should be noted that the following embodiments and features in the embodiments may be combined with each other without conflict.
It should be noted that the illustrations provided in the following embodiments merely illustrate the basic concept of the present invention by way of illustration, and only the components related to the present invention are shown in the illustrations, not according to the number, shape and size of the components in actual implementation, and the form, number and proportion of each component in actual implementation may be arbitrarily changed, and the layout of the components may be more complex.
Referring to fig. 1 and 2, fig. 1 is a flowchart of a mechanical failure prediction method according to an embodiment of the present application. Fig. 2 is a flowchart of a mechanical failure prediction method according to another embodiment of the present application. The invention provides a mechanical fault prediction method, which takes time-varying data as a group of time sequences, can complete prediction by only a small number of data samples, has a simple model, and only needs endogenous variables without other exogenous variables. The dependence on the data quantity is reduced, the accuracy is higher, and the method is suitable for application scenes with smaller data quantity, and the mechanical fault prediction method comprises the following steps:
step S1, selecting data to be predicted, and forming the data to be predicted into a group of time sequences x (t).
Specifically, the data to be predicted in step S1 is selected from an offline database or MySQL database. The data to be predicted is for example: zero offset distribution data of the coils, wear life data, DDV coil bias data, and the like. The time series x (t), (t=1, 2, …).
Step S2, decomposing the time series into eigenmode functions imf of a set of single component signals by empirical mode decomposition i (t) and residual sequence r 0 (t)。
Referring to fig. 3, fig. 3 is a flowchart illustrating an EMD reconstruction of a mechanical failure prediction method according to an embodiment of the present application. Specifically, empirical Mode Decomposition (EMD) extracts a plurality of orders of intrinsic mode functions (Intrinsic Mode Function, IMF) and a residual amount from an original signal by using a local feature time scale of the signal, and each of the decomposed orders of IMF components highlights a local feature of data, and the residual component represents a slow variation amount in the signal. And each IMF is analyzed, so that the characteristic information of the original data can be more accurately and effectively grasped.
Obtaining local maximum values and limit values of the time sequence x (t), and constructing formulas of an upper envelope line h (t), a lower envelope line l (t) and an average value m (t) of the upper envelope line and the lower envelope line by using a cubic spline difference method, wherein the formulas are as follows:
r (t) is the difference between the time sequence x (t) and the mean value m (t) of the upper envelope and the lower envelope, whether r (t) is monotonous is judged, if so, an IMF sequence is decomposed, and the formula for obtaining a plurality of IMF sequences is as follows:
therein, imf i (t) is the ith IMF sequence obtained by empirical mode decomposition, r n (t) is a residual component of the signal after decomposing the n IMF sequences.
Step S3, eigenmode function imf of the single component signal i (t) and residual sequence r 0 (t) performing a stability test, if the stability test is not passed, performing the operation of step S4, and if the stability test is passed, jumping to the operation of step S5.
Specifically, in step S3, if the smoothness test is not passed, the time sequence is a non-smooth sequence, and if the smoothness test is passed, the time sequence is a smooth sequence.
The unit root test refers to checking whether a unit root exists in a sequence. Because there is a unit root, the sequence is a non-stationary time sequence. For one regression process:
X t ＝bX t-1 +a+ε t ，
if the hysteresis coefficient b in this equation is 1, it is called the unity root. When the unit root exists, the residual error in the model is always existed, the process of existence of the unit root in the sequence is not stable, and pseudo regression exists in regression analysis. If no unit root is present, a stable sequence is specified. The H0 hypothesis of the ADF test is that there is a unity root, and if the resulting significance test statistic is less than three confidence levels (10%, 5%, 1%), there is a corresponding (90%, 95, 99%) hold to reject the original hypothesis.
And S4, carrying out differential operation on the non-stationary sequence, establishing an ARIMA model, and jumping to the step S3 for operation.
Specifically, the ARIMA model in step S4 includes ARIMA model parameters d, where d is the difference number.
For example, data that does not satisfy the ADF test requires differential operations to be performed thereon. And then carrying out stationarity test on the delta Xt obtained after the difference operation. If the delta Xt after the difference does not meet the stability condition, carrying out the difference operation for a plurality of times until the ADF test is passed, and obtaining stable data. The difference times are ARIMA (p, d, q) model parameters d. In general, d is not greater than 5, and if the difference number exceeds 5, the data will generate a large distortion, which indicates that the time series is not suitable for prediction by using the ARIMA model.
And S5, judging ARIMA model parameters through AIC criteria or BIC criteria.
Specifically, one of the AIC criterion or the BIC criterion is selected, and the selection can be performed according to the characteristics of the data volume.
The determining ARIMA model parameters by AIC criteria in step S5 includes:
the ARIMA model parameter formula is judged by AIC criterion:
aic=2k-2 ln (L), where L is the likelihood function and k is the model complexity.
The AIC criterion, akaike information criterion, is a measure of the Goodness of fit (Goodness of fit) of a statistical model, and AIC encourages the Goodness of fit of data but avoids overfitting situations as much as possible. Therefore, the model with the lowest AIC value is considered to be the model with the lowest AIC value, and the AIC values of the n models can be calculated at a time, and the model corresponding to the lowest AIC value is found to be used as a selection object on the premise that the selection is made among the n models. Generally, when the model complexity k increases, the likelihood function L also increases, so that AIC becomes smaller, but when k is too large, the likelihood function increases slowly, resulting in an increase in AIC, and the model is too complex, which is liable to cause an overfitting phenomenon.
The determining ARIMA model parameters according to the BIC criterion in step S5 includes:
selecting BIC minimum parameters to obtain p parameters and q parameters:
BIC(p,q)＝minBIC(p,q)。
BIC (Bayesian InformationCriterion) the Bayesian information criterion overcomes the deficiency of AIC criterion, sequentially obtains BICs of AR (1), AR (2), AR (3), … …, MA (1), MA (2) and MA (3) … …, combines to obtain BICs of ARMA models, and selects the model with the smallest numerical value to obtain p and q parameters.
And S6, carrying out residual error detection on the residual errors, and if the residual errors pass the detection, carrying out mechanical fault prediction.
Specifically, the residual in step S6 is the time sequence minus an ARIMA model parameter, where the ARIMA model parameter includes a difference number d, a parameter p, and a parameter q. And carrying out residual error detection on the residual error, judging whether the residual error is white noise, and if the residual error is white noise, indicating that the effective information in the sequence is completely extracted. The residual error check passes, and the next prediction can be performed. If the sequence fails the residual error test, the effective information is not completely extracted, and the extraction needs to be continued.
QQ-plot (Q stands for Quantile) is a graphical method of comparing two probability distributions by plotting the quantiles. First the interval length is selected, the points (x, y) corresponding to the same fraction of the first distribution (x-axis) as the second distribution (y-axis). Therefore, a curve containing parameters, the number of intervals, is drawn. If the two distributions being compared are similar, the QQ plot is approximately on y=x, and if the two distributions are linearly related, the points on the QQ plot fall approximately on a straight line, but not necessarily on the line y=x, and the QQ plot can be used to estimate the position parameter of one distribution as well. In residual error test: the abscissa is the quantile of the normal distribution and the ordinate is the quantile of the residual. If the residual test of the model passes, prediction can be performed. ARIMA prediction is performed separately for each IMF component.
And S7, performing EMD reconstruction on all the predicted sequences of the single component signals to obtain a predicted total value.
Specifically, the EMD reconstruction is performed according to the EMD algorithm flow to obtain the predicted value of the original data.
And S8, comparing the mechanical data in the predicted total value with a set fault threshold value to obtain the residual life of the machine.
Specifically, the principle of the mechanical failure prediction method of the present invention will be described in detail by taking the off-line data of the zero-offset distribution of the parts in table 1 as an example, and table 1 is the offset distribution data of the parts.
Table 1:
the part zero-offset distribution data can be decomposed into three IMF functions IMF 1 (t)、imf 2 (t)、imf 3 (t) and a residual sequence r 0 (t)。
For these four groups of single signal components, imf 1 (t)、imf 2 (t)、imf 3 (t)、r 0 And (t) performing ADF test to determine that the model parameters d are 0, 2, 3 and 5 respectively.
The models for determining the four sets of single component signals using the AIC criterion, BIC criterion are ARMA (2, 0), ARIMA (2, 1), ARIMA (1, 3, 4), ARIMA (3, 5, 4), respectively.
And respectively predicting the four groups of single component signals by using the model.
And (3) carrying out EMD reconstruction on the four groups of single-component signal prediction results to obtain a prediction total value.
Groups 15 to 23 were predicted using groups 1 to 14 of data in table 1. Comparing with the original data, namely the time sequence, as shown in table 2, the prediction accuracy of the mechanical failure prediction method of the invention is higher, and table 2 is the comparison result of the original data and the predicted data.
Table 2:
in summary, the mechanical fault prediction method of the invention regards time-varying data as a set of time sequences, and only a small number of data samples are needed to complete the prediction, so that the model is simple, and only endogenous variables are needed without the help of other exogenous variables. The dependence on the data quantity is reduced, the accuracy is higher, and the method is suitable for application scenes with smaller data quantity.
The above embodiments are merely illustrative of the principles of the present invention and its effectiveness, and are not intended to limit the invention. Modifications and variations may be made to the above-described embodiments by those skilled in the art without departing from the spirit and scope of the invention. Accordingly, it is intended that all equivalent modifications and variations of the invention be covered by the claims, which are within the ordinary skill of the art, be within the spirit and scope of the present disclosure.
Claims (8)
1. A method of predicting a mechanical failure, comprising:
s1, selecting data to be predicted, and forming the data to be predicted into a group of time sequences x (t);
s2, decomposing the time series into a group of eigenmode functions imf of the single component signals by adopting empirical mode decomposition i (t) and residual sequence r 0 (t)；
S3, eigenmode function imf of the single component signal i (t) and residual sequence r 0 (t) performing a stability test, if the stability test is not passed, performing the operation of step S4, and if the stability test is passed, jumping to the operation of step S5;
s4, carrying out differential operation on the non-stationary sequence, establishing an ARIMA model, and jumping to the step S3 for operation;
s5, judging ARIMA model parameters through AIC criteria or BIC criteria;
s6, residual error detection is carried out on the residual error, and if the detection is passed, mechanical fault prediction is carried out;
s7, carrying out EMD reconstruction on the prediction sequences of all the single component signals to obtain a prediction total value;
and S8, comparing the mechanical data in the predicted total value with a set fault threshold value to obtain the residual life of the machine.
2. A method of predicting mechanical failure in accordance with claim 1, wherein: the data to be predicted in step S1 is selected from an offline database or MySQL database.
3. The method of claim 1, wherein the time series is decomposed into eigenmode functions imf of a set of single component signals using empirical mode decomposition in step S2 i (t) and residual sequence r 0 (t) comprises:
obtaining local maximum values and limit values of the time sequence x (t), and constructing formulas of an upper envelope line h (t), a lower envelope line l (t) and an average value m (t) of the upper envelope line and the lower envelope line by using a cubic spline difference method, wherein the formulas are as follows:
r (t) is the difference between the time sequence x (t) and the mean value m (t) of the upper envelope and the lower envelope, whether r (t) is monotonous is judged, if so, an IMF sequence is decomposed, and the formula for obtaining a plurality of IMF sequences is as follows:
therein, imf i (t) is the ith IMF sequence obtained by empirical mode decomposition, r n (t) is a residual component of the signal after decomposing the n IMF sequences.
4. A method of predicting mechanical failure in accordance with claim 1, wherein: in step S3, if the smoothness test is not passed, the time sequence is a non-smooth sequence, and if the smoothness test is passed, the time sequence is a smooth sequence.
5. A method of predicting mechanical failure in accordance with claim 1, wherein: the ARIMA model in step S4 includes ARIMA model parameters d, d being the differential times.
6. The method according to claim 5, wherein determining ARIMA model parameters by AIC criteria in step S5 includes:
the ARIMA model parameter formula is judged by AIC criterion:
aic=2k-2 ln (L), where L is the likelihood function and k is the model complexity.
7. The method according to claim 6, wherein determining ARIMA model parameters by BIC criteria in step S5 includes:
selecting BIC minimum parameters to obtain p parameters and q parameters:
BIC(p,q)＝minBIC(p,q)。
8. a method of predicting mechanical failure in accordance with claim 7, wherein: the residual in step S6 is the time sequence minus ARIMA model parameters including the number of differences d, the parameter p, and the parameter q.
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