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4. CONCLUSION
As a result, samples of bitumen in their quality charac- teristics, namely, softening temperature, needle penetration depth fully comply with the standard, and for individual indicators, such as elongation, brittle temperature, exceed the requirements of the above standard. According to the data obtained, there is a general tendency to improve the properties of bitumen obtained by the oxidation of activated fuel oil. At the same values of the softening temperature, the penetration decreases, and the fragility temperature does not noticeably change. The resulting sol- vates and associates lower the total energy of the system, which leads to an increase in the softening tempera- ture. On the one hand, the heat resistance of bitumen should not be less than the maximum operating tempera- ture, the high softening temperature hampers their use as binders in asphalt mixtures (bitumens with a high soften- ing point, and, therefore, the mineral filler surface is poorly
enveloped by high viscosity). In our opinion, the activation of fuel oil allows the creation of conditions in the oxidation process under which mobile unpaired conduction electrons are almost completely localized in colloidal particles of bitumen, that results in their stabilization. Coagulation and precipitation of crystals of the asphaltene fraction during ageing, in this case, are mostly kinetically and sterically hindered and practically do not occur.
Acknowledgments: The work is performed accord- ing to the Russian Government Program of Competitive Growth of Kazan Federal University.
References
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8. Kemalov, A.F.,2013. Creation of chair high-viscosity oil and nat- ural bitumen’s at the Kazan Federal (Volga region) University—A step to future competitive technologies of development of heavy oil hydrocarbonic raw materials of the Republic of Tatarstan. The Recent Trends in Science and Technology Management. The Collec- tion Includes the Recent Trends in Science and Technology Manage- ment, edited by A. F. Kemalov and R. A. Kemalov, May, Held by SCIEURO in London 09–10, London, pp.247–258.
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Received: 1 January 2019. Accepted: 11 March 2019.
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Printed in the United States of America
Computational and Theoretical Nanoscience Vol. 16, 5254–5260, 2019
Diagnostic Signal Informativeness Increase
Damir Afgativich Kharlyamov
1∗, Ilnar Fargatovich Suleimanov
1, Alsu Ildarovna Sabirova
1, Evgeniy Aleksandrovich Penkov
2, and Ruslan Flyurovich Kalimullin
21Kazan Federal University, Kazan, 420008, Russia
2Orenburg State University, Orenburg Oblast, 460018, Russia
Modern requirements for the operation of cars lead to the need to improve the efficiency of their maintenance. Diagnosis as an element of the maintenance process allows you to provide informa- tion about the technical condition of a particular element, which allows you to respond in a timely manner to the technical condition change of a diagnostic object with minimal resources. In this paper, we consider the way improving the diagnostic signal quality. It is known that a diagnostic signal must meet several requirements. The most important requirement is informativeness, which shows the decrease of uncertainty about the technical condition of an object, represented by a pri- ori entropy after information application from this diagnostic signal, measured during the diagnosis.
There are the methods for a diagnostic signal conversion, which allow to get rid of the noise enter- ing it to a different degree or present it in such a way to facilitate the signal analysis process. Three methods are considered in the work: direct spectrum obtaining, signal envelope spectrum obtaining, and adaptive filtering. The analysis of these methods led to the conclusion that adaptive filtering has the greatest efficiency potential. We have proposed the method that is based on adaptive filter- ing, but with additional operations. In the course of the diagnostic signal studies and the adaptive filtering algorithm, we found that it is possible to set the function to be detected as a variable, as well as several parameters that affect the result quality. Based on this, a new method for a useful signal extraction was proposed. The results of the work were checked on a signal simulating a car gearbox signal. The results show that the method allows you to obtain the necessary knowledge about a defect, which can be used in the diagnosis. The developed method allows to increase the information content of the diagnostic signal by suppressing its other components. The results of the proposed method correlate with the results of other methods for general cases, i.e., when the ratio of the useful signal to noise is such that high sensitivity of the method is not required to identify the useful signal.
Keywords: Diagnostic Signal, Diagnostic System, Car Maintenance, Gearbox Fault Diagnosis, Diagnosis.
1. INTRODUCTION
Diagnosing of the car gearbox (GB) as an element of the power unit transmitting torque from the engine is an urgent task, because untimely detection of a malfunction in it leads to costly repairs. The control of GB techni- cal condition by complete disassembly is not an effective way because of high labor costs. Therefore, maintenance is considered a promising area in terms of actual condition, where the resource of a part and its timely replacement is used to the maximum. Without developed diagnostic sup- port (DS), this method is practically impossible. By devel- oped DS, we mean the presence of a diagnostic signal (DS) that meets certain requirements; effective diagnostic
∗Author to whom correspondence should be addressed.
methods with a high-quality diagnostic model, diagnos- tic algorithm and software; diagnostic tools to minimize labor costs for DS measuring, DS preliminary process- ing, fault detection, etc. In this paper, we consider the way to improve the quality of GB DS. It is known that DS must meet several requirements. The most important requirement is informativeness, which shows the decrease of uncertainty about the technical condition of an object, represented by a priori entropy after applying information from this DS measured during the diagnosis process. The level of controllability of modern gearboxes makes vibra- tion acceleration of the housing walls the most effective diagnostic tool for bearing assemblies and gear diagnos- ing. But even in such a DS there are interferences that complicate its analysis. However, we have the opportunity to influence the measured DS, i.e., to improve its quality
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before use the information that it carries, applying various processing methods that reduce a priori entropy. If a DS is any function that contains a useful part and a noise one, then it is possible to transform it in such a way, influenc- ing the operator, that the resulting function has a minimum noise component:
fDP∗ =A·fDP (1) where Ais the transformation operator; fDP is the diag- nostic parameter undergoing conversion. In this case, the conversion suboperator is understood as the algorithm or a set of algorithms (processing methods) that comply the function to another function.
The development of such methods which allow to increase the information content of DS is one of the most important areas of technical diagnostics [1–5].
2. METHODS
2.1. Obtaining DS “Direct” Spectrum
The most common way of DS processing, but not in all cases informative, is the transition to the time-frequency function without additional operations. If you use this tool to analyze the technical condition of the gear, then it is quite effective. But during bearing assembly diagnosis, this method is applicable at the stages where a defect already has a strong development, while the overall level of the spectrum rises compared to the normal state. Most often, the operation of GB with such a level of defect devel- opment is unacceptable, therefore, the use of this method without additional operations is impractical. Let’s consider the vibration spectrum of four-speed gearbox wall, where there is a crack on the gear tooth of the third gear. Mea- surement mode: 1500 rpm (25 Hz)—the frequency of input shaft rotation. DS from the sensor has the form shown on Figure 1.
Without a priori knowledge, it is extremely difficult to determine this defect by “direct” spectrum. Since this defect is very small on the scale of the entire system, the energy released during impact interaction of parts at the defect site is relatively small.
(b) (a)
Fig. 1. DS in (a) time and (b) frequency representation.
Fig. 2. The scheme for obtaining of the DS envelope spectrum.
Fig. 3. DS after processing with a band-pass filter.
2.2. Obtaining the Spectrum of the DS Envelope This method is quite effective to diagnose various defects of the GB, also during the early stages of development.
Before receiving the DS envelope, it is necessary to pass it through the filter, which to some extent complicates this method, because you need to know the filter bandwidth limits. The scheme of this method is presented on Figure 2.
Knowing the frequency of the defect manifestation, we choose a band-pass filter with the boundaries of 2–4 kHz and let the DS pass through it. The processed DS is shown on Figure 3.
On the graph, you can notice the areas of the defect manifestation. However, it should be noted that in this form it is extremely difficult to analyze the DS, only the
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Fig. 4. DS envelope function and its spectrum.
presence of complete a priori knowledge allows us to give a qualitative assessment of the defect in this case. There- fore, the next step is to obtain DS envelope function and its spectrum (Fig. 4).
Knowing the design parameters of the bearing, it is pos- sible to calculate the frequency of defect manifestation, which is of interest, and using this knowledge, to analyze the spectrum of the DS envelope (Fig. 4). However, there are the moments that make it difficult to use the method:
—selection of filter bandwidth;
—low sensitivity at low signal-to-noise ratios;
Fig. 5. DS processing scheme with adaptive filter.
Fig. 6. The signal obtained after DS processing with adaptive filter.
—the practical impossibility of the entire frequency band determination related to a defect;
—low automation of the process.
2.3. DS Processing with Adaptive Filter
As we noted above, an important component of the pro- cessing method is the ability to give high-quality results with a small signal to noise ratio. An adaptive filter from this point of view is one of the most effective methods, due to the presence of a tunable filter core [6–8]. The DS pro- cessing scheme by an adaptive filter is shown on Figure 5.
A DS consisting of a useful signalsand noisen0, which is not correlated withx, is provided to input. The signal n1, correlated withn0, but not correlating with the useful signal, is also provided to input.
The output of the filtery is formed as follows [9]:
yk=
N−1 i=0
hikn1k−i (2)
Fig. 7. The signal obtained after DS processing by an adaptive filter with a poorly correlated functionn1.
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Fig. 8. The functionn1, supplied to adaptive filter input.
The filter coefficients are changed according to the for- mula [9]:
hk+1i=hki+·eknk−i i=01N−1 (3) whereis the parameter of the convergence step.
The output signal, which is the error function is equal to [9]:
ek=sk−yk (4) wheresk=xk+n0k—the processed signal.
Fig. 9. The signals received at different parameter values of the functionn1.
Let’s apply the adaptive filter to the DS, which has already been analyzed by two other methods, and compare the results. As a correlated signal, we take the impulse function, because a priori, we know its appearance without exact characteristics. This function is selected in such a way that it correlates with the useful signal. As the result of processing in the DS, the noise component is suppressed to the maximum and only the useful component remains.
Figure 6 shows the function obtained after DS processing by the adaptive filter.
As each iteration passes, the filter coefficients are adjusted. The output function allows the most effective assessment of a defect. But such qualitative results are obtained in the presence of the functionn1, which corre- lates as much as possible with the defect signal; however, in practice, we do not have such a qualitative function and the use of the standard algorithm leads to poor-quality results.
The result that is obtained when a poorly correlated functionn1is fed to the input of the adaptive filter can be seen on Figure 7. This signal does not give any informa- tion about a defect, in some sense it can be misleading:
we see repeated bursts that can be interpreted as shock pulses, but in fact the repetition frequency of these pulses does not correspond to the actual frequency of 618 Hz. We conducted the studies in the course of which they revealed important components that strongly affect the final result.
Let’s consider the first three, which directly relate to what
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(a) (b)
Fig. 10. The graph of (a) the functionkand (b) the output signal envelope.
kind of functionn1 will have—this is the frequency of its oscillations fs, the pulse repetition frequency fr and the shift(Fig. 8).
Let’s consider the effect of each of these parameters on the output signal. We will compare with the refer- ence signal presented on Figure 6. For the function n1, we will successively change the value of the parameters fs=1500 Hz,fr=420 Hz, and=10 samples. Figure 9 shows the results obtained during processing. In all cases, the deviation of the functionn1parameters from the opti- mum leads to the loss of signal quality at the output of the adaptive filter. It should be noted that these results were obtained taking into account the fact that at a non-optimal value of one parameter the others were accepted as opti- mal, otherwise the results are extremely uninformative.
Let’s consider some more important components, but now they affect not the input function n1, but the adap- tive processing algorithm itself. It is known that the order of the filter core and the convergence step parameter also affect the final result. Besides, the number of itera- tions also makes influence. Figure 10(a) shows the change
(a) (b)
Fig. 11. The graphical view of the DS from the sensor after processing by the developed algorithm (a) and its spectrum (b).
ofkfrom the filter core parameter (N) and the conver- gence step value (). It can be seen that the graph of the function has differences and local maxima and minima, which means that the choice of these two indicators leads to different results.
Even during the selection of the remaining indicator optimal values considered by us, with an insufficient num- ber of iterations, the output signal does not reach its maxi- mum amplitude, and this can be observed on Figure 10(b).
This means that it is necessary to choose the right num- ber of iterations (niter). Based on the foregoing, we can conclude that the adaptive filter is a fairly effective tool for DS processing, but there are also the moments that limit its use. I.e., there are six components (parame- ters), controlling which you can control adaptive filter effectiveness [10–11].