Kiselyov Alexander Yurievich

Master thesis

"Usage of the wavelet analysis method to control the technical state of the piston compressors"

Contents

1. Introduction
2. Review of existing methods of vibroacoustical control
3. The problems of appling the wavelet analysis method for the piston compressors diagnostics
4. Short results description
5. Conclussion
6. Bibliography

        Last decades functions with the schedule such as a small wave are successfully used for decomposition of signals instead of traditional (long) sine waves. Though concepts of wavelet and wavelet decomposition are rather new, they have already found wide applications in processing signals. Popularity of the given subjects promptly grows.
        The wavelet theory is powerful alternative to the Fourier analysis and gives more flexible technics of processing of signals. One of the basic advantages of the wavelet analysis consists that it allows to notice well located changes of a signal whereas the Fourier analysis of it does not give - in Fourier factors the behaviour of a signal for all time of its existence is reflected. The deep and beautiful mathematical theory of wavelets is developed.
        The purpose of work is reduction in expenses for maintenance service and reception of the most full information on a technical condition of piston compressors that allows to make repair work and replacement of the equipment in due time.
        The vibroacoustical control system of a technical condition of piston compressors should make diagnostics, not breaking normal work of the equipment to determine defects and to predict damage.
        Application of the wavelet analysis method of signals of vibration of piston compressors allows to make deeper diagnostics and to find out defects which with the help of alternative methods to reveal it is not obviously possible.

        "The methods and means for condition assessment were developed step by step. At first, different parameters of machines were controlled, then condition monitoring was used, and, finally, diagnostic and predictive systems were developed. With each new system type, the customer gains new possibilities to perform condition based maintenance.
        The Control Systems are used to measure a number of parameters for comparison with standard levels. Condition Monitoring Systems present additional information on the development of machine parameters with time, reveal tendencies, and predict possible changes of parameters. Condition Diagnostics Systems use the analysis of measured signals to identify the possible defect type, severity and defect location. An even more difficult problem is solved by the Condition Prediction System. This problem is the prediction of the possible development of the existing combination of defects, forecasts of residual service life and prediction of non-failure operation time.
        Recently, the term monitoring has been referred to as the application of the complete set of procedures for condition assessment, although some of the existing condition monitoring systems do not identify defect types nor do they predict defect development. For this reason, monitoring will be further referred to as the control of main parameters, analysis of their trends, and forecasts of possible changes. Diagnostics will be referred to as the identification of defect types and prediction of their development.
        The first group includes the test diagnostic methods. These methods require some external excitation of the object or the use of special signals to scan the object. The condition of the object is estimated by the analysis of the external signal distortions during its interaction with the object. The parameters of the external signal are well known and only the distortions imposed by the an object are considered. These methods are based on the rather simple information techniques and are widely used in condition diagnostics of various units during manufacturing or shut-down periods of the equipment.
        The second group contains the function (operation) diagnostic methods. These methods are used for the analysis of natural signals emitted by a machine in its normal operation. The sources and formation of the emitted signals are considered in this case, but not the distortions of the signals during their propagation through the machine. Moreover, the possible distortions may significantly complicate the analysis of the measured signal and the method itself. The information derived from the distortions of the emitted signals are used only in a limited number of function diagnostic problems.
        Next, we will consider the information techniques used only in the functional diagnostics. The number of these techniques is not very large and the variety of condition diagnostic systems is defined only by the combination of the techniques used.
        The simplest of the basic techniques is the overall level technique based on the power and amplitude measurements. Temperature (temperature variance), pressure, noise, vibration and many other parameters can be used as a diagnostic signal. Here the condition of the equipment is derived by the comparison of the measured signal values with the standard levels.
        The next step in the development of the overall level technique is the frequency technique which is based on signal conditioning prior to the use of overall level measurements. In this case, only the components in the measured signal within a certain frequency band are considered . The frequency analysis technique is used in both condition monitoring and diagnostics of machines and for breakdown protection as well. For example, frequency technique is used for electric arc protection by measuring high-frequency components in the current. Another example is machine protection by the vibration at rotation frequency. Electronic filters are not the only filters that are used to detect different frequency components. Resonance sensors of current, vibration, noise, light flux etc. can be used as well. A stethoscope is the simplest example of this kind of sensor. It transforms the low-frequency vibration of the machine unit into the noise perceived by human ear.
        One more technique is the Phase and Time technique which is based on the comparison of the shapes of the signals measured in constant intervals. This technique is used successfully to control the condition of reciprocating machines with several identical parts (cylinders and pistons) loaded at constant intervals. For example, consider Fig. 1 which presents the vibration signal of a automobile engine. The operation quality of each of the cylinders can be estimated by the shape of the vibration signal.

Fig. 1 – Vibration spectrum of automobile engine measured at the point between cylinder 2 and 3

        Another technique is used to compare the shape of the signal with a standard shape. This is a Spectrum technique that is based on narrow-band spectrum analysis. Here the diagnostic information can be found in the relationship between amplitudes and phases of certain components and their harmonics. This technique is applied for the analysis of vibration, noise, pressure as well as current and voltage from electric machines.
        The above techniques had been in use to control steam engines for the last century. Only the spectrum technique became widely used in the middle of the present century with the invention of relatively simple spectrum analyzers for the analysis of signals. Nowadays, this technique became widely used in condition monitoring and control systems for machines and equipment.
        All of the above techniques have a common limitation for condition diagnostics when you need to detect incipient defects. The problem is that variations of the measured parameters typically exceed the changes indicating incipient defects even in similar appearing non-defective machines. The results of vibration data statistics on good machines of various types give an example of this. These results were proved by independent research in many countries. It was found that a standard variation in many spectrum components lay in the range of 20 dB, i.e. differences of 10 times, and for some components, even higher. At the same time, the defects on the initial stage of their development can produce a considerably smaller influence, changing the values of their typical parameters by only two to three times.
        Development of measurement means and computer engineering during recent years makes possible the partial solution of the problems of condition monitoring and diagnostics by creating systems for machine and equipment monitoring, based on the diagnostic techniques discussed above. Such systems are intended for on-line control (monitoring) of the diagnostic parameters of a particular machine or equipment. They have special modes for adaptation on the initial operating stage when defects are, as a rule, absent. During this stage, they also detect and evaluate the influence of the machine modes and environment, such as temperature, features of power or fuel supply on the parameters monitored. This reduces the probability of a false alert by the monitoring system due to the changes of operating modes or environment.
        The means of data measurement, analysis and input are part of any diagnostic technique based on any signal processing method. Three main stages can be listed in the development of the diagnostic instrumentation.
        The first stage is related to the initial development of diagnostics by vibration and acoustics. At that stage, the human sense organs were the means for machine conditions assessment using noise and vibration. The human ear can perceive and analyze the acoustic signals at audio frequencies. Vibrations of mechanisms at these frequencies always produce a sound. At lower frequencies, you can perceive vibration by hand. Selectivity of vibration analysis can be provided by using stethoscopes that already existed for hundreds of years. Until the last several decades, it was human abilities that defined the primary development of the diagnostics by using vibration and noise signals.
        The next stage came after creation of infrasound measurement instrumentation and spectral analyzers. It was in 1940s and 1950s when, with the appearance of such instruments, intensive research in signal analysis intended for the solution of diagnostics tasks started. In the 1960s and 1970s, significant results in machine condition diagnostics were achieved. Not only did shock pulse and enveloping methods that allow condition diagnostics by single vibration measurement appear, but also the development of diagnostic methods based on narrow-band spectrum analysis appeared as as well. During these years, numerous investigations of different defects influence on machine operation and their diagnostic signals were made. The results of these investigations showed that vibration signal contains most of the diagnostic information and other signal types just duplicate the information which the vibration signal contains already. In addition, evidence were obtained that defects start to develop long before breakdown situations occur. On many types of machine units, the defects start to develop during the first half of the machine's service life. At essentially the same time, defects start to influence the vibration of the machine units. The main problem of the detection of changes produced by defects in the vibration signal is to separate changes introduced by the defects from those due to the changes in loads, rotation speed, temperature variations and other machine and environment parameters. This is the most difficult problem in machine condition diagnostics.
        The third stage of the diagnostic instrumentation development was occurred with the fast progress in computer hardware and technologies. Digital spectrum analyzers appeared on this stage. They allow the simultaneous analysis of hundreds of frequency bands. A that time, expert systems and later automatic diagnostic and condition prediction systems appeared that can replace an expert in diagnostics of different machine types. The appearance of powerful personal computers stimulated the development of new diagnostic techniques based on statistical methods for pattern recognition that are partially used for vibration and acoustic machine diagnostics.
        All means for measurement and signal analysis incorporate three types of devices with different functions. The first one is a vibration transducer or microphone which transforms mechanical oscillations into an electrical signal. The second is a filter that select the signal components in the desired frequency band. The third is a detector used for the evaluation of the magnitude (power) of the selected components. The filter is not necessarily connected after the transducer nor it is always an electronic circuit. It can be acoustic filter, e.g. resonator, or mechanical filter, e.g. flexible padding, installed before the transducer. Different instruments may contain different combinations of these devices according to the technique they use. Structures of the basic kinds of devices for the control and diagnostics of machines and the equipment on vibration or noise are shown below.

Fig.2 – Structures of the basic kinds of devices for the measurement and analysis of vibration and noise signals

        The simplest instruments are devices for measuring the overall level and peak factor, i.e. the shock pulse detector. If there are no special requirements for the frequency band of the measured signal, there may be no filter in the device for overall level measurements. The mechanical resonator typically is made of a metal bar with the resonance at the frequencies higher than 25 KHz. It can be found in most of peak factor devices. Such a high frequency of the resonance decreases the resonator dimensions and allows getting higher peak factor values. The reason for this is that, at high frequencies, the decay time constant in vibration components excited by friction forces that define the RMS value of the signal is minimal.
        The simplest devices discussed above had affordable prices at all stages of instrumentation development, therefore for a long time, practical diagnostics was oriented to them. Recently, the fast development of the computers and significant decreases in their prices allow the use of all the methods discussed in this paper including the more sophisticated diagnostic techniques. Digital signal analyzers are practically equal in price to the simple analog devices, dislodging them from diagnostic use.
        The most frequently used measurement instruments based of the computers include waveform, spectrum, and envelope spectrum analyzers. The Waveform analyzer is used to measure the amplitudes and phases of the signal components and a comparative analysis of the particular signal waveforms that are defined by the shaft rotation angle. These analyzers are widely used for the diagnostics of the reciprocating machines and rotors during balancing. The Spectrum analyzer is used to monitor all types of machines and equipment. The Envelope spectrum analyzer is applied for the analysis of periodic changes in time of the power of random signals.
        The personal computer with an analog to digital converters can be considered as the most accessible instrument for noise and vibration measurements. Such an instrument allow to use any of considered diagnostic techniques or their combinations. Professional quality sound cards can be used for this purpose. Some companies produce specialized computer boards and corresponding software.

Fig.3 – Structure of entrance device

        Such means of measurement allows to use any of the considered information technologies or their combinations. As the listed devices with small completion it is possible to apply professional sound cards. Special entrance devices which structure is resulted on fig. 3, released by a number of firms and the corresponding software to them can be also used." [4]

        Application of the wavelet analysis method for research vibroacoustical signals allows to avoid bulky mathematical calculations and considerably to reduce time for processing of results. However, despite of seen simplicity of algorithm, it nevertheless does not allow to make processing of signals in real time. Such opportunity is given only at use of superfast means of measurement and processing of signals.

        As a result of the lead researches it has been developed the algorithm and the software, allowing to make processing the signals which have been written down on the personal computer as wav files, and also to display results as sequence of readout. Further it is planned to realize algorithm which fully automates process of diagnostics of object.

        As a result of researches principles of construction of the vibroacoustical control systems, feature of the control of technical condition of rotating machines, and in particular, the piston compressor are investigated. A number of mathematical methods which are used for the analysis of signals of vibration is considered, their merits and demerits are marked.
        For a basis for the analysis of signals the wavelet analysis method, as the most suitable for a task in view has been chosen. The given method due to "fast" algorithms allows to make processing of discrete signals with the big speed that makes its irreplaceable at realization of algorithm on the computer.
        The software is developed, allowing to make the wavelet analysis of signals. The initial data for the analysis are represented as wav files of format Windows PCM as most popular format for representation of the sound data. The analysis of signals is made by means of wavelet decomposition of signals with the help of algorithm of Mala and representation of results as a set of factors and the form convenient for visual perception. The detailed description of software functioning, the description of the basic algorithms of work and the interface of the user is resulted.

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