Analysis process and transformation of non-stationary diagnostic signals to reduce the degree of their non-stationarity and the subsequent synthesis of neural network predictive model based on them are considered. The software which allows to apply the developed methods for processing of signals of diagnostics of transmission of the helicopter and on their basis to build the forecasting model for the solution of practical problems of technical diagnostics is developed.
Preventing machinery failure is an important component of the maintenance activities of most engineering systems. For quality control of a technical product, at the end of its production and during design tests technical diagnostics is carried out.
Automation of decision-making in the process of technical diagnosis is an urgent task, as it helps to reduce the load on the human operator, as well as provides efficiency and speed of decision-making and reduces the dependence of complex technical systems on the negative impact of the human factor.
A promising basis for solving the problems of automation of diagnosis are intelligent information technologies that are able to build models for examples – experimental observations "input - output" and extract knowledge from the data in the learning process.
The paper considers the process of diagnosing the helicopter transmission. The helicopter is a complex and valuable technical product. Therefore, after designing the test sample is tested on the stand for a large number of hours. During these tests, changes in the vibration level of the sample are monitored. As a result of such tests, a large amount of data is accumulated in the form of diagnostic signals.
A sharp increase in vibration negatively affects the sample, which can lead to its failure. This entails material costs and the need to suspend testing. Therefore, having a system that can predict the vibration level for a certain time in advance will help to improve the testing process.
The basis of such a system can be used an intelligent model of data-driven [
The goal of the work is to develop methods for converting diagnostic signals to reduce their dimension, allocating the necessary component and reducing the degree of their non-stationary for further synthesis of neuromodels based on them.
The objective of this study is to predict these signals using neural network models. 2
Consider the problem of diagnosing the helicopter transmission [
For monitoring the technical condition of the helicopter used systems like Health
and Usage Monitoring Systems (HUMS) [
Important in HUMS is the ability to assess the technical condition of critical elements of the transmission, using the data of vibration signals that were recorded during the flight or ground tests.
A neural network model will be used as a predictive model. Formally, the problem of neuromodels synthesis can be presented in this form.
Suppose given the original sample as a set of prece-dents (instances) <xt, yt> is a set of S precedents characterizing dependence yt(xt), at the moment t, t = 1, 2, …, T, where xt={xst}, y={yst}, s = 1, 2, ..., S, characterized by the set of N input features {xtj}, j = 1, 2, ..., N, where j is a number of feature, and output feature y. Each s-th precedent can be noted as <xst, yst>, where xst={xstj}.
Then the problem of model synthesis of dependence yt(xt) will be considered in search of such structure F() and adjusting such values of parameters w of a model which will satisfy the model quality criterion f(F(), w, <xt, yt>) → opt, where opt – is a symbol of optimum. Usually, the criterion of learning quality of neuromodels is defined as a function of model error (1): Е 1 S
( y5 F ( , x5 ))2 min . 2 s1 (1) 3
In most research methods, it is assumed that the signal, and in General, any time series is stationary, and the time dependence is considered possible to take into account a variety of non-statistical methods. For example, the series is decomposed into three components: trend, cyclic and random. A trend is a component of a series that changes over a long period of time due to the influence of fundamental factors. The cyclic component changes in time with a certain period according to the course of repetitive processes. The random component includes all the last components that can not be assigned to one of the first two groups. The use of such separation for technical diagnostic signals may not provide optimum results due to the following factors.
First, the component can be quite complicated. For example, its trend characteristics may be nonlinear and non-linear, as predicted in most trend allocation methods. Secondly, in the tasks of technical diagnostics there is always a "white noise", the smallest error of forecasting which is equal to its dispersion. Thus, the series is divided into three parts, although this separation is fuzzy, the cyclic component can become a trend at intervals of less than a period, and the trend and the cyclic component can go into the category of random component.
The solution of the problem of stationary signaling of technical diagnostics is
possible, but in most cases it entails a significant change in the structure of the signal
itself. And the evaluation of the technical product on the received signal can not
provide the necessary level of its quality. Metrics that are based on the components of
its internal structure, for example, based on its wavelet decomposition [
To estimate the degree of unsteadiness of the signal, we will use the dilated
Dickey-Fuller criterion [
From the results it is possible to observe a sufficiently high degree of unsteadiness of the studied signals. To find the relationship between the current and the previous signal values, we use the auto-correlation function. Autocorrelation is a correlation of the function itself with a certain variable of an independent variable. The autocorrelation function is defined as:
R f ( ) f (t) f * (t )dt , where the function f (t ) integrates into a product with a complex conjugate and a function displaced by a certain value .
The graph of the signal received on the intermediate gearbox (axial direction of measurement), which characterizes the state of the first gear drive of the intermediate gearbox is shown in Fig. 1. The graph also contains a 95% confidence interval to determine the statistical significance of the autocorrelation coefficient.
The carried autocorrelation analysis confirmed the proposed assumption of the presence of cyclicity in the signal. The presence of auto-correlation complicates the use of a number of methods of analysis of time series. Therefore, to reduce autocorrelation, elimination is used to shift from correlation of levels to correction of deviations from trends - residues (for example, the conversion of a time series into a number of values of differences between its adjacent members). This approach can not be applied in this case due to the above reasons for impossibility to change the initial structure of the diagnostic signal.
Another solution to this problem is to split the signal into several components, which will eliminate cyclicity and maintain the original signal strength. 4
To reduce the non-stationary time series, methods can be applied that will lead to its
breakdown into a certain number of smaller time series, in such a way that they are
absent, explicitly, as a component of cyclicity [
We process the processing of these signals to obtain the values of the rotational frequency by counting the number of times the signal changes in 1 second (the discretization frequency of the rough signal 7200 Hz). The graph of the signal received on the intermediate gearbox (axial direction of measurement), which characterizes the state of the first gear drive of the intermediate gearbox is shown in Fig. 3.
After processing the signal, you can observe the progress of 18 cycles of diagnosis. You can also observe the change in operating modes. In one mode of operation, the speed does not change significantly. The processed signals of rotation of the turbocharger rotor right engine demonstrate similar results. This is because the left and right engines duplicate each other to increase reliability.
It is proposed to allocate from the general signal of diagnosing the intervals during which the diagnosis took place in one mode of operation. For example, we isolate from the general signal for diagnosing the intervals during which the diagnosis took place in the second mode of operation. It is proposed to perform autocorrelation analysis for the received signals.
The graph of the signal received on the intermediate gearbox (axial direction of measurement), which characterizes the state of the first gear drive of the intermediate gearbox in the second mode of operation of turbochargers is shown in Fig. 4 The graph also contains a 95% confidence interval to determine the statistical significance of the autocorrelation coefficient.
Fig. 4. Autocorrelogram of signal received on the intermediate gearbox (axial direction of measurement) in the second mode of operation of turbochargers
The performed autocorrelation analysis demonstrates the absence of expressed cyclicity in the signal. This indicates a qualitative breakdown of diagnostic signals, which should help to reduce the unsteadiness of newly formed signals.
To quantify the degree of non-stationarity of the signals, we calculate the values of the Dickey - Fuller criterion for them. Table 2 contains the values of the extended Dickey - Fuller criterion for part of the signals obtained from the signals of diagnosing the helicopter transmission by the proposed methods gearbox in the second mode of operation of turbochargers.
There is a significant decrease in the values of the Dickey - Fuller criteria, which indicates a decrease in the degree of signal non-stationarity after the proposed partition. Also, there is a much smaller scope of the test values than in table 1, this makes it possible to assume that the degree of non-stationarity of the signals corresponds to the non-stationarity of the diagnosis process in this mode. All this makes it possible to better use the signals for the synthesis of predictive models. 5
A four – layer recurrent neuron network with an input layer, two hidden layers with GRU-cell (Fig. 5) and an output layer with one linear neuron was chosen as a neu-ral network model. GRU [15] is a simplified model of a well – known LSTM cell with significantly fewer parame-ters. Through this, learning GRU is easier than LSTM, so it is gaining popularity in many real-world tasks.
ht-1 reset gate
Whr Wxr
x rt
Whh Wxh cand. cell
state tanh Whu Wxu update gate h't ut + x 1ht xt
Fig. 5. The structure of the GRU-cell
At the input of the GRU-cell receives a vector x, which contains the current values of the signals. The output of the cell is calculated by the following formulas (3)-(6): ut (Wxu xt Whu ht1 bu ) , rt (Wxr xt Whr ht1 br ) , ht tanh(Wxh xt Whh (rt ht1 )) , (6) (7) (8) ht (1 ut ) ht ut ht1 .
(9)
The synthesized neural network model was tested and optimized on a sampling of signals during the diagnosis of the helicopter transmission at the second mode of the turbochargers of the engines. The total initial sample contained data collected in total for 1010 seconds for 22 diagnostic signals. She was divided into a training sample - 1 - 800 seconds, and the test - 801 - 1010 seconds.
As the input data of the models, the data for all signals for a given time window width were used. Data on one of the 22 signals with a given forecasting horizon, that is, a forward shift in the time scale of 120 seconds, were used alternately as initial data. The neural network error was calculated by formula 1. Neural network training was conducted over 250 epochs.
To improve the quality of the forecast, optimization of neural network hyperparameters was carried out. The results are given in tables 3 - 5.
The prediction error is 0.0167 for the second mode of operation of turbochargers, which is 13.45 % in percentage terms. The forecast error for a signal without division into operating modes is 0.1096, which is 28.56% in percentage terms.
Therefore, if it is necessary to predict the state of the helicopter transmission for all modes, it is recommended to divide the signal by the proposed method, to predict each part of the signal using a predictive model and combine them on the basis of information about the duration of the operating modes. 6
In the conducted research of methods of analysis and transformation of non-stationary signals of diagnosing the method of reducing the degree of non-stationarity of the received signals based on expert information about the modes of operation during the diagnosis cycle was proposed.
The effectiveness of the method of reducing the degree of unsteadiness of signals based on expert information about the modes of operation during the diagnosis cycle is evidenced by a significant optimization of the value of the Dickey-fuller criterion after its application. This method, unlike most, does not require changing the internal structure of the signal, and works only by splitting the signal into several other signals, which can then be combined.
On the basis of processed signals, a neural network was synthesized to predict the state of the helicopter transmission and its hyperparameters were configured.
The results are planned to be used to improve the diagnostic quality of the helicopter transmission.
The method of transformation of nonstationary signals and the construction of neural network models developed and applied in the investigated method can be used to solve problems in which it is necessary to predict the future state of the object, by its diagnostic signals. 14. MacKinnon, J. G.: Critical Values for Cointegration Tests. In: R. F. Engle and C.
W. J. Granger, eds., Long-Run Economic Relationships: Readings in Cointegration, Oxford University Press, pp. 267–276 (1991) 15. Goodfellow, I., Bengio, Y., Courville, A.: Deep Learning, MIT Press (2016) http://www.deeplearningbook.org