CN107085750A - A kind of mixing dynamic fault Forecasting Methodology based on ARMA and ANN - Google Patents
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Abstract
Set up the linear submodels of ARMA the invention discloses a kind of mixing dynamic fault Forecasting Methodology based on ARMA and ANN, including step and set up ANN nonlinearities models, so as to obtain mixing mixed model.Compared with prior art, the present invention combines advantages of the ARMA in the advantage and ANN in terms of pull-in time sequences part in terms of Nonlinear Time Series are predicted, influence of the real time data to model parameter is considered during prediction, with reference to ARMA and ANN prediction process, set up real-time dynamic forecast model, it is to avoid the single respective limitation of model.
Description
Technical Field
The invention relates to an equipment fault prediction method, in particular to a hybrid dynamic fault prediction method based on ARMA and ANN.
Background
The forecasting is an emerging discipline, which analyzes and infers the future development state and trend of a research object under the guidance of relevant theories and methods according to historical data and state data, and the forecasting technology is widely applied in the fields of industry, commerce, finance, meteorology and the like. The state prediction technology is used for evaluating the current state of the equipment and predicting the future state according to the running state of the equipment. Prediction techniques can be classified into three categories according to the degree of application, prediction accuracy and associated costs of the prediction method: the universality of the three methods in engineering application is weakened in sequence, but the prediction precision is improved in sequence, and the difficulty and the cost related to the prediction precision are increased.
The existing prediction technology has made great progress in theoretical research and practical application, but the existing prediction method has many limitations, the prediction process has great dependence on a mathematical model, cannot meet the actual requirements of a complex system, and cannot obtain a satisfactory result when the mathematical model of the system is inaccurate. Most prediction models belong to static models and lack self-learning capability, the prediction models are obtained through one-time modeling, model parameters are kept fixed, the influence of newly added samples on the model parameters is not considered, and the problems of inaccuracy of single-step prediction and invalidation of multi-step prediction of complex equipment generally occur.
In the current fault prediction method, an autoregressive moving average model is suitable for capturing a linear part of a time sequence, and when the problem of complex nonlinearity is solved, the error is often very large; while neural networks work well when predicting non-linear time series, neural networks perform poorly when predicting linear time series.
Disclosure of Invention
In order to overcome the defects of the prior art and combine the advantages of the ARMA and the ANN methods, so that the time sequence can be well predicted, and the prediction precision is improved, the invention provides a hybrid dynamic fault prediction method based on the ARMA and the ANN.
The technical scheme of the invention is realized as follows:
a hybrid dynamic fault prediction method based on ARMA and ANN comprises the steps of
S1: according to the characteristics of sample data, carrying out stabilized data preprocessing on the sample data to generate a data sequence;
s2: estimating an autoregressive order and a moving average order of the data sequence according to the properties of the autocorrelation coefficient and the partial correlation coefficient of the data sequence and an AIC (automatic interference coordination) criterion, and determining a model of the data sequence;
s3: estimating model parameters according to a least square method, and determining the relation between an observed value at the current moment and a historical moment observed value and a white noise sequence;
s4: using the data sequence to check whether the model reaches the precision, if not, returning to the step S2 until a reasonable ARMA model is obtained, and further obtaining a static multi-step prediction error;
s5: substituting the historical data into a prediction equation of the ARAM model to obtain data of the next moment;
s6: repeating the steps S3-S5 to perform L-step prediction, and adding predicted data into the data sequence;
s7: if the predicted circulating speed measurement is less than the number of predicted data when L-step prediction is carried out, turning to step S8; otherwise, obtaining the prediction result of the linear part, and turning to the step S9;
s8: substituting the actual observed value into the L-th predicted value to serve as a time sequence, and turning to the step S3 to perform L-step prediction of the next cycle;
s9: training an ANN model by using the static multi-step prediction error, obtaining a prediction residual according to the prediction result, taking the prediction residual as time sequence data of the ANN model, and repeating the steps S5-S8 to obtain a prediction result of a nonlinear part;
s10: and obtaining a prediction result of the hybrid model according to the prediction result of the linear part and the prediction result of the nonlinear part.
Further, in step S10, the prediction result of the hybrid model is the prediction result of the linear part + the prediction result of the non-linear part.
Compared with the prior art, the method has the advantages that the method combines the advantages of ARMA in capturing the linear part of the time sequence and the advantages of ANN in predicting the nonlinear time sequence, considers the influence of real-time data on model parameters in the prediction process, combines the prediction processes of ARMA and ANN, establishes a real-time dynamic prediction model, and avoids the respective limitations of a single model.
Drawings
FIG. 1 is a flow chart of a hybrid dynamic fault prediction method based on ARMA and ANN of the present invention;
FIG. 2 is a logic flow diagram of a hybrid dynamic fault prediction method based on ARMA and ANN according to the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Since the autoregressive moving average model is suitable for capturing the linear part of the time series, the error tends to be large when solving the complex non-linear problem. While neural networks work well when predicting non-linear time series, neural networks perform poorly when predicting linear time series. Therefore, the hybrid model combining the ARMA and the ANN method is provided, so that the hybrid model has the advantages of the two models simultaneously, the time series can be well predicted, and the prediction precision is improved. The hybrid model comprises an ARMA linear sub-model and an ANN non-linear sub-model.
Referring to fig. 1, the hybrid dynamic fault prediction method based on ARMA and ANN according to the present invention includes steps of
S1: according to the characteristics of sample data, making stabilization and data pretreatment, and setting the treated data sequence asI.e. training data;
let the time series X ═ X1,x2,…,xl) And t is the current moment, and the hybrid dynamic L-step prediction is carried out on the current moment. Initial time k is t, j is 1(j is the number of prediction cycles), and N1 is the number of prediction data.
S2: model identification, namely determining a model structure, estimating an autoregressive order n and a moving average order m according to the properties of an Autocorrelation Coefficient (ACF) and a partial correlation coefficient (PACF) of a rotating speed data sequence and an AIC criterion;
the autoregressive moving average model (ARMA) is a time sequence model, which not only can reveal the regularity of dynamic data and predict the future value thereof, but also can research the relevant characteristics of the system from multiple aspects.
For a normal, steady, zero-mean time series { xtIf xtThe value of (a) is related to the value of the previous n steps and the excitation of the previous m steps, and a general ARMA model is formed by combining an Autoregressive (AR) model and a Moving Average (MA) model.
Where n and m are the autoregressive and moving average orders, which are abbreviated as ARMA (n, m), if n is 0, the model is the MA model, and if m is 0, the model is the AR model. Real numberCalled auto-regressive coefficients, real number θiFor the moving average coefficient, the sequence { a }tIs a white noise sequence.
S3: estimating model parameters according to a least square method, and determining the relation between the observed value at the current moment and the observed value at the historical moment and the white noise sequence;
in the process of predicting the time sequence by the ARMA model, firstly, the time sequence is differentiated to obtain a stable random sequence, then, the order of the model is determined, a proper model is selected, then, the model parameter is estimated, the parameter value of the model is calculated, and finally, the model is subjected to adaptability test and model application.
S4: using training dataChecking whether the model reaches the precision, if so, obtaining a reasonable ARMA model so as to obtain a static multistep prediction error etrain (t) (namely training data of ANN), and turning to the step 5; otherwise, turning to the step 2;
s5: comparing historical dataObtaining k +1 time data instead of prediction equation
An input layer: input vector X ═ X1,x2,…,xl) Monitoring data for the condition of a device or systemAnd certain preprocessing is performed, such as noise reduction, normalization and the like. An intermediate layer: the intermediate layer is also called hidden layer, and can be a layer or a multi-layer structure, and is formed by wijAnd wjkConnecting the input layer and the output layer. An output layer: the output value is a predicted value, the number m of nodes of the output layer is the total number of the predicted result, Yt＝(y1,y2,…,yt)。
S6: if k +1-n is less than L, k is equal to k +1, wherein L is to perform L-step hybrid dynamic prediction, add the predicted data into the sequence, go to step 3, and re-estimate the parameters; otherwise, turning to step 7;
the neural network mainly realizes the prediction function by two methods, the first method takes the neural network as a function approximator to perform fitting prediction on parameters, and the second method considers the dynamic relation between input and output and uses the dynamic neural network with feedback to establish a dynamic model for the parameters to perform prediction. In predicting the time series, a neural network with feedback is generally used for prediction.
In the process of predicting based on the neural network model, firstly, selecting reasonable training, testing and analyzing samples by taking state monitoring data as samples; then setting a training model through network parameters; then testing the trained network model by using the test sample, and checking the network performance; and finally, predicting by using the model and the analysis sample.
S7: if jL<N, when the j-th cycle is performed, the number of predicted cycles is smaller than the number of predicted data when L-step hybrid dynamic prediction is performed, and the step 8 is switched; otherwise, obtaining the predicted resultTurning to step 9;
assume that X ═ X for time series input1,x2,…,xl) It is true that the expected output is Yt＝(y1,y2,…,yt). Firstly, predicting a time series by using an ARMA model, wherein the time series comprises the following steps:
whereinFor ARMA predicted values, the model is ordered by using AIC criterion, and AIC function is defined as: let the autocorrelation coefficientThen
Wherein, N is the sample capacity,are maximum likelihood estimates corresponding to various algorithms. Respectively establishing models for different values of n and m from a low order to a high order, carrying out parameter estimation, and comparing AIC values of the models to make the models reach minimum values, wherein the models are optimal models, and the formula is shown as formula 3:
writing formula 3 as follows, and performing parameter estimation by using least square method
Wherein,and calculating the value of the model when the sum of squared errors is minimum, namely solving the minimum value of the following formula.
The derivative of the previous trial yields an estimate of the parameter βThen there is
The linear submodel prediction remainder can be obtained by the following steps:
s8: obtaining L in step S7, substituting the actual observed value for the previous L-step predicted value as a time series, and proceeding to step S3 to perform L-step prediction for the j-th cycle + 1;
s9: training the ANN model with etrain (t) of step S4, the prediction from ARMA of step S7Obtaining a prediction residual YN(t) repeating the steps S5-S8 as time series data of ANN to obtain the prediction result of the nonlinear part
Remainder Y obtained by equation 6N(t) establishing a neural network model, establishing a non-linear sub-model part:
whereinTo predict the result, wj(j ═ 0,1,2 …, q) and wij(i-0, 1,2, …, p; j-0, 1,2 …, q) is the connection weight of the neural network, p, q represent the number of nodes in the input layer and the intermediate layer of the network, respectively, and the output layer is usually 1 for one-step forward prediction, b0And b0jIn order to be a term of the offset,tfor the prediction error at time t, g is the activation function of the network, usually expressed as a logistic function, i.e.:
s10: byAndand obtaining the prediction result of the mixed model:
by integrating equations 1, 6 and 7, the expression of the obtained mixed model is as follows:
wherein,in order to achieve the end result of the prediction,for ARMA prediction, YN(t) is the residual of ARMA and is used as input to the ANN model, which is trained,and predicting the result for the ANN model.
Since the autoregressive moving average model cannot capture the nonlinear part of the time sequence, the remainder obtained by the formula 9 contains the nonlinear component of the time sequence, the remainder is modeled by using a neural network, and the two results are combined to obtain higher prediction accuracy.
While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention.
Claims (2)
1. A hybrid dynamic fault prediction method based on ARMA and ANN is characterized by comprising the following steps
S1: according to the characteristics of sample data, carrying out stabilized data preprocessing on the sample data to generate a data sequence;
s2: estimating an autoregressive order and a moving average order of the data sequence according to the properties of the autocorrelation coefficient and the partial correlation coefficient of the data sequence and an AIC (automatic interference coordination) criterion, and determining a model of the data sequence;
s3: estimating model parameters according to a least square method, and determining the relation between an observed value at the current moment and a historical moment observed value and a white noise sequence;
s4: using the data sequence to check whether the model reaches the precision, if not, returning to the step S2 until a reasonable ARMA model is obtained, and further obtaining a static multi-step prediction error;
s5: substituting the historical data into a prediction equation of the ARAM model to obtain data of the next moment;
s6: repeating the steps S3-S5 to perform L-step prediction, and adding predicted data into the data sequence;
s7: if the predicted circulating speed measurement is less than the number of predicted data when L-step prediction is carried out, turning to step S8; otherwise, obtaining the prediction result of the linear part, and turning to the step S9;
s8: substituting the actual observed value into the L-th predicted value to serve as a time sequence, and turning to the step S3 to perform L-step prediction of the next cycle;
s9: training an ANN model by using the static multi-step prediction error, obtaining a prediction residual according to the prediction result, taking the prediction residual as time sequence data of the ANN model, and repeating the steps S5-S8 to obtain a prediction result of a nonlinear part;
s10: and obtaining a prediction result of the hybrid model according to the prediction result of the linear part and the prediction result of the nonlinear part.
2. The hybrid dynamic fault prediction method based on ARMA and ANN as claimed in claim 1, wherein the prediction result of the hybrid model is the prediction result of the linear part + the prediction result of the non-linear part in step S10.
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Cited By (13)
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| CN108734341A (en) * | 2018-04-27 | 2018-11-02 | 广东电网有限责任公司 | A kind of self-organizing Electric Load Forecasting reporting method based on time series arma modeling |
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| CN111612226A (en) * | 2020-05-12 | 2020-09-01 | 中国电子科技集团公司电子科学研究院 | Group daily average arrival number prediction method and device based on hybrid model |
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| CN113255965A (en) * | 2021-04-26 | 2021-08-13 | 大连海事大学 | Intelligent processing system for prognosis of degradation fault of radar transmitter |
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| CN109614742A (en) * | 2018-12-25 | 2019-04-12 | 中国海洋大学 | A kind of sea level height duration prediction algorithm |
| CN111190045A (en) * | 2019-12-27 | 2020-05-22 | 国网北京市电力公司 | Voltage abnormity prediction method and device and electronic equipment |
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