DOI: 10.12731/wsd-2015-8.2-6 УДК 519.246.87
АНАЛИЗ КАЧЕСТВА РЕГИСТРАЦИИ ПАРАМЕТРОВ ПРОИЗВОДСТВЕННОГО ПРОЦЕССА
Ивнев Д.А., Васильков Ю.В.
Измерение, контроль и запись показателей производства ведутся на каждом современном предприятии, однако зачастую уделяется недостаточно внимания качеству регистрации. В случае некорректно установленных периоде дискретизации и точности записи оператором могут быть сделаны ложные выводы при анализе процесса. Кроме того, точность записи существенно влияет на удобство работы с величинами и на размер необходимой для регистрации памяти. Исследование реальных производственных данных, измеренных как в заводской лаборатории, так и непосредственно полевым уровнем автоматизированной системы управления, показывают необходимость изменения параметров регистрации. Результаты корреляционного и спектрального анализа, а также применение теоремы Котельникова определяют условия корректной регистрации величин. Выявленные устойчивые зависимости между процессами указывают на общую природу их изменения. Результаты регрессионного анализа могут быть использованы для математической формализации описания процессов, а также для выбора режима управления процессами.
Ключевые слова: точность измерения; частота дискретизации; теорема Котельникова; экспериментальные данные; корреляционный анализ; спектральный анализ.
ANALYSIS OF INDUSTRIAL PROCESS PARAMETER REGISTRATION QUALITY
Ivnev D.A., Vasilkov Y. V.
Measuring, controlling and recording of production processes are performed in every modern factory plant, however there is often no focus on
registration quality. If incorrect time intervals and recording accuracies are used, false conclusions can be made by process analysis. In addition, recording accuracy has an essential effect on the operational comfort and on the memory size required for the data recording. The investigation of real process data, which are measured in the laboratory and by automated control system on the field level as well, shows the registration parameters must be changed. The results of correlation and spectral analyses along with the application of the Nyquist-Shannon theorem define the conditions of correct value registration. The identified stable relations point to mutual reason of changing. The regression analysis results can be applied to mathematical process description and used for control mode selection.
Keywords: measuring accuracy; sampling rate; Nyquist-Shannon theorem; experimental data; correlation analysis; spectral analysis.
Introduction
Acquisition and analysis of data strongly affects process control. The study of process parameter changing shows the relationship between production activities, assures the development of superior control systems and grants a higher product quality. The result of data analysis depends on registration parameters. The more data that is available, the more reliable the result of analysis is. However, having a larger amount of data requires a greater hard disk drive volume.
Object of study
Searching for optimal registration parameters and demonstrating the possibility to reduce the recorder resources while preserving the valuable information about the object.
Research methods and materials
Discrete-time sampling of analogue quantities of production processes lead to partial information loss. The Nyquist-Shannon theorem [1] (the Kotelnikov theorem in Russian literature [2]) defines the minimal signal sampling fre-
quency, at which the discrete signal can be restored in analogue signal without distortion
f ■ = 2f, (1)
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where f is the highest frequency enclosed by the signal spectrum.
As a spectrum characteristic is frequency curve usually used [3, 4, 5]. Since the real signal contains plenty of harmonics, there is a need to detect the harmonic with the highest frequency. There is a compromise in identification of the carrier waves related to the useful signal and harmonics related to the random noise. As is customary, there is a rule to define the maximal frequency: the harmonic curve of useful signal usually has an amplitude peak value not less than the similar value of the most expressed harmonic [6]. The harmonics, which have an amplitude value less than the assigned value are referred to measure noise. Generally, there are some peaks in the high frequency area on the frequency curve; there are fewer peaks when the data are well smoothed.
The correct frequency line building is shown in works [4, 7 and 8]. The building of this curve is concerned with data pre-processing, which is described in work [9]. It is worth nothing that there are demands to data sample: ergodicity, stationarity, and sufficient length of data sample [10, 11, 12]. These data properties have to be checked before spectral and correlation characteristics ratings. There is an experimental process data series represented (figure 1).
Mass flow, /h,
MP 1 «
1 1 h r 1
i F'
T y
0 5000 10000 15000 20000 25000 30000 35000 40000 45000 50000 55000 60000
Fig. 1. Initial series of registered data
The presented data series has sufficient length of sample: more than 60 thousand points with 10 seconds time interval, however this large amount of
dat demands an essential computational capability which is why the initial series is substituted by the corresponding. The spectral characteristics must not be transformed appreciably. The comparison of the frequency curves of initial and corresponding series, which has sample time 30 minutes, shows the possibility of the replacement (figure 2).
Fig. 2. The spectral characteristics of initial and corresponding series
The difference between two curves is essential when the peak values have to be defined, but the frequencies of the extrema were not shifted considerably, so the initial series with a sample time of 10 seconds can be substituted with the corresponding series with a sample time of 30 minutes (figure 3).
The observable series also has sufficient length, and the points with numbers between 150 and 350 meet the requirements of stationarity and ergodicity, therefore the correlation and spectral analyses can be realized [13, 14, 15]. The data are processed by programs "Time series analysis" IT-Accent® [16] and MS Excel.
370 360 350 340 330 320 Mass flow t/h
k Nh M J* 'Ayv^ijJt uAfA
Mf /1 v
11. r
m
50 100 150 200 250 300 350
Fig. 3. Corresponding data series
The estimation of measuring inaccuracy demonstrates the maximal dilatation from the average value within 1.5% of measurement range. Therefore the measuring device has an accuracy class not higher as 1.5, so it makes sense to register only the integer values without significant figures after the decimal mark by this measurement range [17, 18]. Thus, there is no need to save the data with higher accuracy. Nevertheless the process data are registered without a rounding of measure and they are registered with ten significant digits after the decimal mark now. The investigation showed that rounding of the measurement value to the significant digit, in this case to the integer value, does not change the forms of spectral and correlation characteristics [9, 19].
Spectral characteristic analysis shows that the observable series has three pronounced harmonics with frequencies 0, 0.011 and 0.016, therefore the signal power is mostly fixed on these three frequencies [20, 21] (figure 4).
0.005 0.010 0.015 0.020 0025 0.030 0.035 0 040 0.045 0.050
Fig. 4. Frequency curve of corresponding series
Since the series under study has a sampling time of 30 minutes, the maximum frequency on the frequency graph is
f = 30 • 60 • 0,016 = 28,8 s-1. (2)
The minimum frequency according to the Nyquist-Shannon theorem, by which the useful information will not lost, is
f. = 2 • f = 2 • 28,8 = 57,6 s-1. (3)
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Results of research and discussion
The calculations presented show that the process parameter should be measured with a sample time 57 seconds, not 10 seconds. This time guarantees that such a frequency is sufficient for the registration of the process parameter
without loss of useful information. With this factor, recording experimental parameters requires 5.7 times less memory span. Results of research show that production processes are often logged in excessive amounts, and there is the possibility to reduce the number of stored values. Despite the fact that the recording frequency reduction leads to data loss, the number of registered measurements is sufficient for proper process analysis.
In conclusion
Scientifically substantiated selection of registration mode precipitates the treatment and the analysis of the process parameter relations. In control software engineering, the discrete sampling time and the measurement precision must be considered. Storing only the statistically significant numbers along with the correct sampling time greatly reduces financial investments, which can have a great impact considering the large amount of parameters registered after years of production.
The authors thank Th. Kolbe Technical Director LLC HeidelbergCement Russia for giving data and D. Westerman for helping with translation and data handling.
References
1. Basarab, M. A. Tsifrovaya obrabotka signalov na osnove teoremy Uitte-kera-Kotel'nikova-Shennona [Digital signal handling based on Whittaker-Ko-telnikov-Shannon theorem]. Moscow. : Radiotekhnika Publ, 2004. 72 p.
2. Bikkenin R. R., Chesnokov M.N., Teoriya elektricheskoy svyazi [Electrical coupling theory]. Moscow: Akademiya Publ., 2010. 329 p.
3. Kovalenko D.A., Zavidey V.I., Pechenkin V.I. Primenenie korrelyatsionnogo analiza pri aktivno-teplovoy diagnostike vnutrennego sostoyaniya silovykh transformatorov [Application of correlation analysis by active-thermal diagnostics of power transformer internal state]. Vmire nauchnykh otkrytiy [In the World of Sc
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