METHODS OF LARGE-SCALE SIGNALS TRANSFORMATION FOR DIAGNOSIS IN NEURAL NETWORK MODELS

Context. The problem of dimensionality reduction of diagnosis signals for their use in neural network models is considered. The object of the study was the process of transformation of diagnosis input signals for their subsequent use in the synthesis of predictive models


ABBREVIATIONS
GRU is a gated recurrent unit; HUMS is a Health and Usage Monitoring Systems; LSTM is a long short-term memory; NN is a neural network; RNN is a reccurent neural network; NOMENCLATURE C is a condenser capacity; ε is a ripple factor; F() is a neural network model structure; f() is a user criterion characterizing the argument quality relatively to the problem being solved; H is a sampling rate of the signal envelope; N is a number of time steps in signal; n is an order of the filter; R is a resistance of the resistor; σ is a sigmoid activation function; T n (x) is a Chebyshev polynomial of the n-th order; τ is an averaging time of the signal; tanh is a hyperbolic tangent activation function; ω 0 is a cutoff frequency; ω(t) is a signal envelope; w is a set of controlled (adjusted) parameters of the neural network model; x s j is a value of j-th input feature x j , characterizing the instance x s ; y s is an output feature value associated with the instance х s ; y s* is a calculated output feature value for the s-th instance on the neural model output; х s is s-th instance of a sample; x(t) is an input signal; x f (t) is a signal received as a result of the recursive filtering stage; ψ(t) is a Hilbert transform of signal.

INTRODUCTION
To automate decision making and forecasting in the tasks of technical and medical diagnostics, it is necessary to have a model of dependence of the solution on the descriptive features characterizing the recognized instance (observation of the state of the object or process at a certain point in time).As a rule, the modern diagnostic process is carried out over a period of time, during which observations are recorded and can be presented in the form of sets of diagnostic signals.
One of the most popular and powerful tools for constructing models based on diagnostic signals is artificial radial basis NN and RNN [1], which can learn by precedents, providing their generalization and knowledge extraction from data.
The object of study was the process of transformation of diagnosis input signals for their subsequent use in the synthesis of predictive models.
The process of neural model building is typically time-consuming and highly iterative.This is caused by that training time and accuracy of the NN model are essentially dependent on the dimensionality and quality of the used training sample.Therefore, to improve the speed of construction and quality of the neural model, it is necessary to reduce the dimension of the input signals of diagnosis, by isolating the necessary components from them and further averaging them, thereby ensuring the preservation of their basic properties.
The subject of study is the methods of reducing the dimension of the input signals of diagnosis and isolation of their components, which characterize the state of the individual elements of the object of diagnosis.
The known methods of reducing the training sample [2] aren't optimal for applying them to diagnostic signals with a high sampling rate due to the large requirements for time and computational resources and the complexity of their implementation in practice.
The purpose of the work is the conversion of diagnosis signals as a result of which new signals will be obtained, which in turn will be used in the construction of NN predictive models and will significantly reduce the synthesis time of the model by reducing their dimension and the allocation of the necessary components that characterize the state of the individual elements of the object of diagnosis.

PROBLEM STATEMENT
Consider the problem of diagnosing the helicopter transmission.Preventing machinery failure is an important component of the maintenance activities of most engineering systems.Helicopters are constantly exposed to periodic loads and vibrations that initiate and propagate the occurrence of damage in many components of the equipment.This is due to the design of the helicopter and the presence of complex mechanical systems, such as the inventive rotor, control rotor, main gearbox and other transmission elements.In most cases, the failure of these systems lead to catastrophic situations.HUMS are used to monitor the technical condition of the helicopter [3].These systems make possible to detect damage in the transmission components and predict their residual life.
In this paper, we set the task of long-term forecasting of the state of the helicopter transmission during the ground test.This type of test allows the use of significant computing power, which is important when working with a large number of signals, which are measured at a high sampling rate and for significant periods of time.However, with this type of test, it is necessary to build predictive models that will work correctly on long-term periods of time.
Formally, the problem of neuromodels synthesis can be presented in this form.
Suppose given the original sample as a set of precedents (instances) <x t , y t > is a set of S precedents characterizing dependence y t (x t ), at the moment t, t = 1, 2, …, T, where x t ={x s t }, y={y s t }, s = 1, 2, ..., S, characterized by the set of N input features {x t j }, j = 1, 2, ..., N, where j is a number of feature, and output feature y.Each s-th precedent can be noted as <x s t , y s t >, where x s t ={x s tj }.Then the problem of model synthesis of dependence y t (x t ) 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, <x t , y t >) → opt, where opt -is a symbol of optimum.
In case when the original sample has a big dimensionality before model building we need to decide a problem of less size subsample selection from the original sample (given: X=<x t , y t >, t = 1, 2, …, T, needed: X′=<x′ p , y′ p >, p = 1, 2, …, P, where P << T, f(<x′ p , y′ p >, <x t , y t >) → opt).
To build the model in the problem we used the data of vibration diagnostics of the helicopter transmission containing fifteen piezoelectric sensors to monitor the level of vibration mounted on the transmission components, such as: rotor shaft cover, coupling flange of the upper and lower part of the gearbox, drive flange of main rotor, intermediate gearbox and tail gearbox.At the mounting point, there are 3 sensors that allow monitoring vibration parameters in mutually perpendicular planes.

REVIEW OF THE LITERATURE
The problem of long-term forecasting of the state of the helicopter transmission includes the solution of a complex of subtasks of forecasting the state of individual elements of the transmission [4].Usually this problem is solved by predicting the next N values of a certain diagnostic signal [5].
However, this approach has shortcomings that make it difficult to put into practice.First, the input signal has low informativeness regarding the state of a particular transmission element.Secondly, the condition of the transmission element is usually characterized not by one, but by several different diagnostic signals.Third, the input signals have a large sampling rate.
At the same time, there is a need to build predictive models based on big data to ensure satisfactory prediction accuracy.These limitations make the process of synthesis and training of models based on computational intelligence such time-consuming and computational resources.
Signal transformation is an important problem in the construction of analytical and predictive models that work based on computational intelligence.The development of such models is associated with the need to process big data [1][2]6].Typically, the input selection data which represent the signals which describe the investigated processes may contain redundant and uninformative information [7][8].The use of such information in the synthesis of models leads to an increase in their complexity, redundancy, reduction of generalizing capabilities and can make the synthesized model unusable due to the need for large computational resources.
Usually, to solve this problem, the data is preprocessed to exclude from the training sample redundant features and instances.Most of the known methods use a greedy or stochastic search strategy [9].Both of these strategies aren't optimal for working with time sequences that are represented by signals with a high sampling rate due to the large time and computational resources and the complexity of their implementation in practice.
One of the most effective tools for data analysis is signal processing [10].It has a large number of means to allocate the necessary components of the signal, its normalization and averaging.

MATERIALS AND METHODS
To solve these problems, two methods for converting input signals based on signal processing methods have been developed and can be used to monitor and predict the state of a certain transmission element when specifying the signal processing parameters.
The method of signal transformation to obtain values for the vibration overload parameter is proposed to be used to obtain an assessment of the state of the transmission element with the vibration overload parameter.
Initialization stage.Set input signal x(t).
Recursive filtering stage.To apply to the input signal x(t) type I Chebyshev filter to select from it the necessary frequency band, which characterizes the state of the transmission element.According to [10] the amplitude frequency characteristic of the type I Chebyshev filter is defined as (2): Selection of the signal envelope stage.Select the signal envelope to obtain the absolute value of the signal.For this, according to [11], the signal received as a result of the previous stage can be represented as an analytical signal with addition to the real signal x f (t) of its Hilbert transformation as imaginary part (2): from here signal envelope is defined as (3): Selection of the envelope signal is carried out using a peak detector [12], which is used to allocate the maximum and minimum values of the signal envelope.
Signal averaging stage.Get the average value of the signal amplitude over τ seconds by the formula (4): ., , The method of signal transformation to obtain values for the vibration speed parameter is proposed to be used to obtain an assessment of the state of the transmission element with the vibration speed parameter.
Initialization stage.Set input signal x(t).Recursive filtering stage.To apply to the input signal x(t) type I Chebyshev filter to select from it the necessary frequency band, which characterizes the state of the transmission element.
Signal integration stage.To integrate the signal by the method of RC-circuit [13] with the number of averaging points N to change the parameter to the vibration speed parameter.An RC circuit is an electrical circuit consisting of a resistor R and a capacitor C. Integration is performed by the formula: Selection of the signal envelope stage.Select the signal envelope (2)-( 3) to obtain the absolute value of the signal.Selection of the envelope signal is carried out using a peak detector which is used to allocate the maximum and minimum values of the signal envelope.
Signal averaging stage.Get the average value of the signal amplitude over τ seconds by the formula (4).
The developed methods of signal transformation allow selecting the necessary components from the input signals.After the necessary components are selected, the signal is averaged.
With the use of a band-pass filter, signals are cleared of low-frequency and high-frequency components, which have low informativeness in the original signals.Further averaging of the signal allows to reduce the influence of random amplitude and noise components of the signal, as well as to reduce its dimension.
This allows the use of processed signals in NN models more efficiently than the original signals.In practice, this will increase the speed of predictive models.
After the transformation of the original input data, a predictive model can be synthesized based on them.
In most HUMS as the predictive model used a feedforward NN [3][4].These models demonstrate their per-formance for short-term forecasting, but as the time window between the input data and the target value of the forecast increases, the quality of the models decreases.
Models of RNN have connections between elements that create a directed sequence.This makes it possible to process successive series of events in time.Unlike multilayer perceptrons, RNN can use their internal memory to process sequences of arbitrary length.
At the moment, there are a large number of models of RNN and new architectures are being developed to solve various problems.In [14] analyzes the main models of RNN to solve the problem of long-term forecasting of the state of the helicopter transmission.
A four -layer recurrent neuron network with an input layer, two hidden layers with GRU-cell (Fig. 1) and an output layer with one linear neuron was chosen as a neural network model.GRU [15] is a simplified model of a well -known LSTM cell with significantly fewer parameters.Through this, learning GRU is easier than LSTM, so it is gaining popularity in many real-world tasks.) ( )) ( tanh( 4 EXPERIMENTS To study the proposed methods of signal transformation, they were implemented in software using WinPOS data processing procedures [16].The NN model was implemented in Python using the PyTorch library [17]. During the experiment, from 15 original input signals, 22 artificial (calculated) signals were isolated and obtained using the proposed methods, which show the state of such transmission elements, such as: the first tooth of the main gear, rotor blade, tail shaft, the first tooth of the intermediate gearbox, the first tooth of the tail gearbox, tail rotor blade, tail rotor.Information about transformed signals is given in the Table 1.For recursive filtering in the proposed methods of signal conversion, a filter of 4-th order with the value of ripple factor ε = 0,3 dB was used.To integrate the signal by the method of RC-circuit, the number of averaging points is N = 800.The signals were averaged over time τ = 1 s.
Four-layer RNN with GRU-cells were used in the experiments.It had 30 neurons in the first hidden layer and 15 neurons in the second.It was trained using the RMSprop method with learning rate 0.01, one train batch contained 40 values [18].
Experiments were conducted during which the historical information on the progress of the 18 cycles of trans-

RESULTS
The frequency band was determined separately for each transmission element, according to its physical parameters.For example, for signal processing by the rotor blade parameter, the filter bandwidth of 1000-2750 Hz was used (Fig. 2).To assess the quality of the forecast, we used the mean squared error of the forecast of the signal by the formula (10): Predictive models were synthesized on the basis of the processed signals.As output signals, during the experiment, all received signals were used alternately.
Predictive models were synthesized on the basis of the processed signals.As output signals, during the experiment, all received signals were used alternately.
For example, the prediction error for the signal received on the intermediate gearbox (axial direction of measurement) and processed with a parameter: first gear drive of the intermediate gearbox is 0.0167, which corresponds to 13.45%.According to expert estimates, this error is acceptable for the problem of predicting the transmission of the helicopter.

DISCUSSION
The use of the proposed methods made it possible to obtain a set of signals for effective prediction of the state of the object of diagnosis.The general condition of the diagnostic object is characterized by a multivariative time series.The most flexible tool for forecasting such series is NN forecasting models.The results shown in table 2 demonstrate that the model built on the basis of the received signals provides the necessary forecasting accuracy.
The advantage of using processed signals is that their dimension is many times smaller than the dimension of the input signals.Also, these signals are more informative for the expert and don't require further processing after receiving the forecast.
The disadvantages of the proposed methods are that in order to obtain high prediction accuracy it is necessary to have a large set of input signals.However, the modern process of diagnosis often has a large amount of historical information in the form of signals with a high sampling rate.
Also, the developed methods can be basic for the development of more specialized methods for predicting individual characteristics of the diagnosis signal.For example, to predict the sharp vibration jumps about the diagnosis of technical objects, which often leads to the failure of the object.
The results of the experiments shown in Fig. 4 and table 2 demonstrate the efficiency and flexibility of the developed methods.Based on this, the proposed methods can be effectively used in practice to predict the state of the object of diagnosis.

CONCLUSIONS
The urgent problem of reducing the dimension of diagnosis signals for the synthesis of data-driven neural network diagnosis models is considered.
The scientific novelty of obtained results is the methods of signal transformation based on signal processing are proposed.They are based on the methods of signal processing, solve the problem of selecting the desired components of the signal, and reduce its dimension.The developed methods can significantly reduce the dimension of the input signals, without reducing their informativeness.This allows to increase the speed of synthesis of NN models based on transformed signals.
The practical significance of obtained results is that the software realizing and used to solve practical regression problems.The experiments have confirmed the efficiency of the developed proposed software and allow us to recommend it for use in practice for the problems of synthesis of models based on precedents, which are presented as signals.

Figure 1 -
Figure 1 -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 (6)-(9): mission tests (cycle duration t = 150 s) was used as a training sample.The input signals were transformed by the proposed methods into signals characterizing the state of individual transmission elements.The purpose of building a predictive model was to obtain a forecast of the state of the transmission element on the next test cycle based on a set of values of time steps (time window) on the current cycle.The size of the sliding time window equal to 3 was used in the experiments.Data about signals of the first 14 cycles were used as training data.Data about the signals of the last 4 cycles were used as test data.

Figure 2 -Figure 3 -
Figure 2 -The example of using the proposed methods for processing the signal from the rotor shaft cover (vertical direction of measurement): a -original signal; b -processed signal

Figure 4 -
Figure 4 -The example of prediction signal values received on the intermediate gearbox (axial direction of measurement) and processed with a parameter: first gear drive of the intermediate gearbox The fragment of the results of conducted experiments for this and other examples is presented in the Table2.

Table 1 -
Information about the signals obtained by the proposed methods