# Criterion for signal smoothing and jump prediction using extrapolation in real-time systems

Стаття | Article

Veronika Niechkina

Igor Sikorsky Kyiv Polytechnic Institute

ni2403kalos@gmail.com

Abstract. The criterion for smoothing random signal changes using a buffer in real-time systems is developed. The problem of the occurrence of rapid spasmodic changes in temperature during the operation of the system for fixing changes in the liquid level in the tank is considered. In the process of solving the problem, a buffering criterion was introduced. Signal changes were written to the buffer.

Keywords : control system, buffering, delay, extrapolation.

## I. INTRODUCTION

There are systems that analyze signal changes. The purpose of such systems is to analyze the value of the measured signal and control processes and objects. During the operation of such systems, short-term processes may occur, accompanied by a sudden change in the measured signal. A sharp change in the measured signal is a local phenomenon and does not characterize the measured process. But the system responds to such changes. The system processes the signal value, which is not a characteristic of the current process [1 - 2]. Such sudden changes in the signal are quite short-lived. The signal will return to the previous value. Information about the signal will get into the system. The system will respond to the jump and process the signal data during the jump. The goal of this work is to eliminate jumps and smooth out the signal. Also, the control system that analyzes the signal changes should stop responding to short-term signal changes. Buffering will delay data processing. Jumps will be processed in the buffer.

## II. CRITERIA FOR DETERMINING THE TIME OF BUFFERING

The introduction of an additional delay in turn increases the response time of the system to changes in the fluid level. Let the system receive data at intervals 1 second, buffer size – n, basic system response delay – ${{\tau }_{sys}}$, maximum allowable delay – ${{\tau }_{\max }}$.

Buffering time:

${{\tau }_{buff}}=n\cdot 1c\quad$

Then, with the introduction of buffering, the new delay will be:

${{\tau }_{\Sigma }}={{\tau }_{sys}}+{{\tau }_{buff}}\quad$

The values ${{\tau }_{\max }}-{{\tau }_{sys}}$ is small for system, the introduction of a buffer the size of which is sufficient for the detection and processing of jumps will cause the delay to be exceeded ${{\tau }_{\max }}$, which is inadmissible. Since the jumps are different from the processes served only in duration, the programmatic jump recognition is not possible without the introduction of buffering [3 – 4].

An additional problem: minimize the delay that is introduced to the system when solving the task.

When buffering is introduced, a delay occurs. It can be minimized if buffering is not continuous. Provided that the signal has changed. If at the end of the accumulation of signal values in the buffer to process them not one by one, but all together in one iteration of the processing cycle, then this approach allows to reduce the total system delay. If the size of the buffer – n, basic system response delay – ${{\tau }_{sys}}$, maximum allowable delay –${{\tau }_{\max }}$, then:

${{\tau }_{\Sigma }}=\max ({{\tau }_{buff}},{{\tau }_{sys}})\le{{\tau }_{sys}}+{{\tau }_{buff}}\quad$

If possible, pick one n, at which ${{\tau }_{buff}}=n\cdot 1c\le {{\tau }_{sys}}$, then:

${{\tau }_{\Sigma }}=\max ({{\tau }_{buff}},{{\tau }_{sys}})={{\tau }_{sys}}\quad$

There will be no further delay in applying the proposed method. It is necessary to formulate a criterion that will determine the possibility of a jump. If for the processes occurring during the operation of the system, it is possible to choose such a method of extrapolation of the next value of the signal that it will give the maximum deviation from the real value obtained at the places of change of the monotone of the signal, then the difference between the real value of the signal and the extrapolated value at each time can use as a buffer criterion [5].

## III. EXPERIMENTAL RESULTS

Consider the process of fixing the change in the liquid level in the tank [6]. The locking system works in real time and has a sensor immersed in some liquid. If the liquid level decreases, the sensor enters the air, its temperature increases due to changes in heat transfer. One of the algorithms of the system responds to this temperature rise and informs the operator about the liquid level decrease. When the liquid level rises again and covers the sensor, its temperature decreases and the alarm goes off. In some cases, rapid abrupt changes in temperature may occur, which can be recognized by the algorithm as a decrease/return of the fluid level and lead to an erroneous alarm. The general view of the signal generated by the system is shown in Fig. 1. If you divide the graph into separate sections, the signal is first constant, then monotonically increasing, then again has a constant plot, then monotonically decreases and becomes constant again, you can approximate the value of the signal by the least squares method, and take the next point on that line, then the value will deviate as much as possible from the actual value obtained at the places of change of monotony. In the course of the work numerous checks were carried out on real signals. The graph of the signal and the extrapolated values is shown in Fig. 2. It shows that the maximum deviation of the extrapolated value deviates from the real signal at the inflection points.

Fig. 1. Graph of the temperature of the liquid level sensor

Figure 2 presents numerous signal values, extrapolated values and deviations of extrapolation from the real signal value. The data confirm that extrapolation can be used as a buffer criterion. Also, by analyzing the deviation, it can be seen that the value at the places of sharp change of the signal is much higher than the deviation at the places of the smooth change of the signal due to the decrease of the liquid level. Therefore, it is possible to set the maximum tolerance value to avoid buffering when the signal changes smoothly.

Fig. 2. Graph of the real and extrapolated values of the signal as it grows

The deviation at the monotone sections of the module does not exceed 1. Therefore, for the presented example of [7 - 8] the input signal, you can use the selected buffer criterion. The following Fig. 3 illustrate the operation of a system of recording fluid level changes in a tank with a time buffer whose duration is determined by the proposed criterion. The actual color value of the signal is displayed in red, and the values transmitted to the handler are shown in blue.

Fig. 3. Smoothing the jump as the signal grows

## IV. CONCLUSIONS

Processes that occur during the test of control systems are accompanied by a sudden change in the measurement signal. Such phenomena force the system to react, which is harmful. It is possible to counteract the impact of the jumps by introducing additional sensors or adding buffering to the communication channel between the sensor and the control system. The introduction of buffering will delay the processing of data. Jumping will be processed in the buffer. The problem of the influence of stubby changes in the measuring signal was solved using the buffer criterion. Using the difference between the actual value of the signal and the extrapolated value at each time point, we recorded the change in the derivative signal during buffering. Processing the buffer after detecting a sudden change in the measured signal is performed by combining the values before and after buffering with one straight line. It was this that made it possible to accurately record the temperature without rapid jumps when changing the liquid level in the tank. The results obtained can be used in measurement and control systems for various objects and processes.

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May 30, 2020