CN107085750A - A Hybrid Dynamic Fault Prediction Method Based on ARMA and ANN - Google Patents

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

A Hybrid Dynamic Fault Prediction Method Based on ARMA and ANN

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 technique

Forecasting is an emerging discipline. It analyzes and infers the future development status and trend of the research object based on historical data and state data under the guidance of relevant theories and methods. Forecasting technology has been widely used in industry, commerce, and finance. , Meteorology and other fields. State prediction technology is to evaluate the current state of the equipment and predict the future state based on the operating status of the equipment. According to the application degree, prediction accuracy and related cost of the prediction method, the prediction technology can be divided into three categories: the prediction method based on reliability theory, the prediction method based on data-driven and the prediction method based on time-dependent physical model. The breadth of application decreases sequentially, but the prediction accuracy increases sequentially, and the difficulty and cost associated with it also increase.

The existing prediction technology has made great progress in theoretical research and practical application, but there are still many limitations in the existing prediction methods. The prediction process relies heavily on mathematical models, which cannot meet the actual requirements of complex systems. , satisfactory results cannot be obtained when the mathematical model of the system is inaccurate. Moreover, most of the forecasting models are static models, lacking self-learning ability. The forecasting model is obtained through one-time modeling, and the model parameters remain fixed. The impact of new samples on the model parameters is not taken into account. For the forecasting of complex equipment, there is usually a single-step forecasting Problems with imprecise, invalid multi-step forecasts.

In the current fault prediction methods, the autoregressive moving average model is suitable for capturing the linear part of the time series, but when solving complex nonlinear problems, the error is often large; while the neural network is better in predicting nonlinear time series, but Neural networks perform poorly at predicting linear time series.

Contents of the invention

In order to overcome the deficiencies of the existing technology and combine the respective advantages of ARMA and ANN methods, so as to better predict the time series and improve the prediction accuracy, the present invention proposes a hybrid dynamic fault prediction method based on ARMA and ANN.

Technical scheme of the present invention is realized like this:

A hybrid dynamic fault prediction method based on ARMA and ANN, including the steps

S1: According to the characteristics of the sample data, perform smooth data preprocessing on the sample data to generate a data sequence;

S2: According to the properties of the autocorrelation coefficient and partial correlation coefficient of the data sequence and the AIC criterion, estimate the autoregressive order and the moving average order of the data sequence, and determine the model of the data sequence;

S3: Estimate the model parameters according to the least square method, and determine the relationship between the observed value at the current moment and the observed value at the historical moment and the white noise sequence;

S4: Use the data sequence to verify whether the model has reached the accuracy, if not, go back to step S2 until a reasonable ARMA model is obtained, and then obtain a static multi-step prediction error;

S5: Substituting historical data into the prediction equation of the ARAM model to obtain data at the next moment;

S6: Repeat steps S3-S5 to perform L-step prediction, and add the predicted data to the data sequence;

S7: If the prediction cycle speed measurement is less than the number of prediction data when performing L-step prediction, then go to step S8; otherwise, get the prediction result of the linear part, go to step S9;

S8: Substituting the actual observed value into the L-th step prediction value as a time series, and turning to step S3 to perform the L-step prediction of the next cycle;

S9: Using the static multi-step prediction error, train the ANN model, obtain the prediction residual according to the prediction result, as the time series data of the ANN model, repeat steps S5-S8, and obtain the prediction result of the nonlinear part;

S10: Obtain a prediction result of the mixed model from the prediction result of the linear part and the prediction result of the nonlinear part.

Further, the prediction result of the hybrid model in step S10=the prediction result of the linear part+the prediction result of the nonlinear part.

The beneficial effect of the present invention is that, compared with the prior art, the present invention combines the advantages of ARMA in capturing the linear part of time series and the advantages of ANN in predicting nonlinear time series, and considers the influence of real-time data on model parameters in the prediction process. Influence, combining the forecasting process of ARMA and ANN, establish a real-time dynamic forecasting model, avoiding the respective limitations of a single model.

Description of drawings

Fig. 1 is a kind of flow chart of the hybrid dynamic fault prediction method based on ARMA and ANN of the present invention;

Fig. 2 is a flow logic diagram of a hybrid dynamic fault prediction method based on ARMA and ANN in the present invention.

detailed description

The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some, not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without creative efforts 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 is often large when solving complex nonlinear problems. While neural networks are good at predicting nonlinear time series, neural networks perform poorly at predicting linear time series. Therefore, a hybrid model combining ARMA and ANN is proposed so that it has the respective advantages of the two models at the same time, so that the time series can be predicted better and the prediction accuracy can be improved. The hybrid model includes two parts: ARMA linear sub-model and ANN nonlinear sub-model.

Please refer to Fig. 1, a kind of hybrid dynamic fault prediction method based on ARMA and ANN of the present invention, comprises steps

S1: Perform stabilization and data preprocessing according to the characteristics of the sample data, and set the processed data sequence as That is, the training data;

Assume that the time series X=(x ₁ , x ₂ ,...,x _l ), t is the current moment, and perform hybrid dynamic L-step prediction on it. Initial time k=t, j=1 (j is the number of prediction cycles), and N1 is the number of prediction data.

S2: Model identification, that is, the determination of the model structure, according to the properties of the autocorrelation coefficient (ACF) and partial correlation coefficient (PACF) of the rotational speed data sequence and the AIC criterion to estimate the autoregressive order n and the moving average order m;

Autoregressive moving average model (ARMA) is a time series model, which can not only reveal the law of dynamic data and predict its future value, but also can study the relevant characteristics of the system from many aspects.

For a normal, stable, zero-mean time series {x _t }, if the value of x _t is not only related to the value of the previous n steps, but also related to the excitation of the previous m steps, then there is a general ARMA model by autoregressive (AR) model and moving average (MA) model.

Among them, n and m are the order of autoregressive and moving average respectively, abbreviated as ARMA(n, m), if n=0, this model is MA model, if m=0, this model is AR model. real number It is called the autoregressive coefficient, the real number θ _i is the moving average coefficient, and the sequence {a _t } is the white noise sequence.

S3: Estimate the model parameters according to the least square method, and determine the relationship between the observed value at the current moment, the observed value at the historical moment, and the white noise sequence;

In the process of predicting the time series by the ARMA model, the time series is firstly differentiated to obtain a stationary random sequence, then the order of the model is determined, the appropriate model is selected, the model parameters are estimated, the model parameter values are calculated, and the model is finally adapted test and apply the model.

S4: Using training data Check whether the model reaches the accuracy. If it is satisfied, a reasonable ARMA model is obtained, so as to obtain the static multi-step prediction error etrain(t) (that is, the training data of ANN), and then go to step 5; otherwise, go to step 2;

S5: the historical data Substitute the prediction equation to get the data at time k+1

Input layer: The input vector X=(x ₁ ,x ₂ ,…,x _l ) is the status monitoring data of the equipment or system, and has undergone certain preprocessing, such as noise reduction, normalization, etc. Intermediate layer: The intermediate layer is also called the hidden layer, which can be one layer or multi-layer structure, and connects the input layer and the output layer through w _ij and w _jk . Output layer: the output value is the predicted value, the number of nodes in the output layer m is the total number of predicted results, Y _t =(y ₁ ,y ₂ ,…,y _t ).

S6: If k+1-n<L, then k=k+1, where L is to perform L-step hybrid dynamic prediction, add the predicted data to the sequence, go to step 3, and re-estimate the parameters; otherwise, go to step 7;

The neural network mainly implements the prediction function through two methods. The first method uses the neural network as a function approximator to fit and predict the parameters. The second method considers the dynamic relationship between input and output, and uses a dynamic neural network with feedback to predict parameters to establish a dynamic model for prediction. In the process of forecasting time series, the neural network with feedback is usually used for forecasting.

In the process of forecasting based on the neural network model, firstly use the state monitoring data as a sample to select reasonable training, testing and analysis samples; then set the training model through the network parameters; then use the test samples to test the trained network model to check the network performance ; Finally use the model and analyze samples to make predictions.

S7: If jL<N, that is, in the j-th cycle, the number of prediction cycles is less than the number of prediction data when performing L-step hybrid dynamic prediction, and go to step 8; otherwise, the prediction result is obtained Go to step 9;

Assuming that the time series input is X=(x ₁ , x ₂ ,...,x _l ), in fact, the desired output is Y _t =(y ₁ , y ₂ ,...,y _t ). First, the ARMA model is used to predict the time series, then:

in is the predicted value of ARMA, and the AIC criterion is used to determine the order of the model. The AIC function is defined as: Let the autocorrelation coefficient but

Among them, N is the sample size, is the maximum likelihood estimate corresponding to various algorithms. Establish models for different values of n and m from low-order to high-order, and perform parameter estimation, compare the AIC values of each model, and make it the smallest model is the best model, as shown in formula 3:

Write Equation 3 in the following form, and use the least squares method for parameter estimation

in, Calculate and solve the value of the model when the sum of squared errors is minimized, that is, find the minimum value of the following formula.

The estimator of the parameter β can be obtained by deriving the above test then there is

Through the above process, the predicted remainder of the linear sub-model can be calculated:

S8: Obtain L through step S7, replace the previous L-step predicted value with the actual observed value as a time series, turn to step S3, and carry out the L-step prediction of the j=j+1 cycle;

S9: Use the etrain(t) of step S4 to train the ANN model, and the prediction result obtained by ARMA in step S7 Obtain the prediction residual Y _N (t), as the time series data of ANN, repeat steps S5-S8, obtain the prediction result of the nonlinear part

Use the remaining term Y _N (t) obtained by formula 6 to establish a neural network model, and establish a nonlinear sub-model part:

in To predict the result, w _j (j=0,1,2…,q) and w _ij (i=0,1,2,…,p; j=0,1,2…,q) are the connections of the neural network Weight, p and q represent the number of nodes in the input layer and middle layer of the network respectively, usually the output layer is 1 for one-step forward prediction, b ₀ and b _0j are bias items, ε _t is the prediction error at time t, g is the activation function of the network, usually expressed by the logistic function, namely:

S10: by with That is, the prediction result of the mixed model is obtained:

Combining formulas 1, 6 and 7, the mixed model expression is obtained as:

in, For the final prediction result, is the ARMA prediction result, Y _N (t) is the residual error of ARMA, and it is used as the input of the ANN model to train the ANN model, Predict the outcome for the ANN model.

Since the autoregressive moving average model cannot capture the nonlinear part of the time series, the remainder obtained in Equation 9 contains the nonlinear components of the time series. Using the neural network to model the remainder, and then combining the two parts of the results will result in a higher prediction accuracy.

The above description is a preferred embodiment of the present invention, and it should be pointed out that for those skilled in the art, without departing from the principle of the present invention, some improvements and modifications can also be made, and these improvements and modifications are also considered Be the protection scope of the present invention.

Claims (2)

1. A hybrid dynamic fault prediction method based on ARMA and ANN, characterized in that, comprising the steps S1: According to the characteristics of the sample data, perform smooth data preprocessing on the sample data to generate a data sequence; S2: According to the properties of the autocorrelation coefficient and partial correlation coefficient of the data sequence and the AIC criterion, estimate the autoregressive order and the moving average order of the data sequence, and determine the model of the data sequence; S3: Estimate the model parameters according to the least square method, and determine the relationship between the observed value at the current moment and the observed value at the historical moment and the white noise sequence; S4: Use the data sequence to verify whether the model has reached the accuracy, if not, go back to step S2 until a reasonable ARMA model is obtained, and then obtain a static multi-step prediction error; S5: Substituting historical data into the prediction equation of the ARAM model to obtain data at the next moment; S6: Repeat steps S3-S5 to perform L-step prediction, and add the predicted data to the data sequence; S7: If the prediction cycle speed measurement is less than the number of prediction data when performing L-step prediction, then go to step S8; otherwise, get the prediction result of the linear part, go to step S9; S8: Substituting the actual observed value into the L-th step prediction value as a time series, and turning to step S3 to perform the L-step prediction of the next cycle; S9: Using the static multi-step prediction error, train the ANN model, obtain the prediction residual according to the prediction result, as the time series data of the ANN model, repeat steps S5-S8, and obtain the prediction result of the nonlinear part; S10: Obtain a prediction result of the mixed model from the prediction result of the linear part and the prediction result of the nonlinear part. 2. A kind of hybrid dynamic fault prediction method based on ARMA and ANN as claimed in claim 1, characterized in that, the prediction result of the hybrid model=the prediction result of the linear part+the prediction result of the nonlinear part in the step S10.