November27, 2022

Abstract Volume: 6 Issue: 2 ISSN:

Biomathematical Analysis on Impedance Measurement During Covid-19 Pandemic

Bin Zhao1*, Xia Jiang2

 

1. School of Science, Hubei University of Technology, Wuhan, Hubei, China.

2. Hospital, Hubei University of Technology, Wuhan, Hubei, China.


Corresponding Author: Dr. Bin Zhao, School of Science, Hubei University of Technology, Wuhan, Hubei, China.

Copy Right: © 2022 Dr. Bin Zhao, This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Received Date: October 27, 2022

Published Date: November 10, 2022

 

 

Abstract

The coating impedance size can reflect the aging degree of the coating to a certain extent, therefore, the measurement of the coating impedance size can monitor the aging degree of the coating in real time. Since the coating is traditionally considered as an insulating medium, its impedance value before aging is as high as 10^8 Ω or more, it is difficult to achieve accurate impedance measurement, and the current generated by loading by voltammetry at low voltage is very weak and easily affected by external electromagnetic interference noise, and the measurement accuracy is low. In this paper, by pluralizing the high impedance, establishing the mathematical model of differential amplification circuit, and then using sinusoidal fitting in which processing, so that the obtained signal is more accurate during COVID-19 pandemic.

Keywords: High impedance measurements, Differential circuits, Sine fitting

Biomathematical Analysis on Impedance Measurement During Covid-19 Pandemic

Introduction

In the industrial field, impedance is an important parameter, and the measurement and analysis of impedance helps us to understand the changes of morphological characteristics of the object under test[1]. For example, in the oil and gas pipeline transmission system, the impedance of the pipeline corrosion protection layer needs to be measured to grasp its service life[2];in the field of biomedicine, the clinical application of bioimpedance technology has a great front[3]; in the field of corrosion monitoring, the monitoring of aircraft coatings, which is an effective means to prevent corrosion of the base metal[4], these belong to the category of high impedance measurement, with an impedance of up to 108 Ω. Therefore, in the processing of these weak signals processing, the idea of sinusoidal fitting is used to process to obtain more information during COVID-19 pandemic.


Differential amplifier circuit mathematical model

The excitation signal is formed by bucking the sine signal generated by filtering, assuming that the bucking scale factor is ????1 and the amplitude of the sine signal before bucking is ????, the excitation signal is expressed as:

????????(????) = ????1????????????????(????????)?1?

 

If the differential amplification is ????2, the output ???????? of the differential amplifier circuit and the input ????????satisfy the following vector relationship;

 

????                           ????

????? = ????2???????? ????? ?2?

 

Translated into a specific functional form of time it can be expressed as:

 

????

???? (????) = ????1????2|???????? | ????????????(???????? + ????)?3?

 

????0: Reference impedance, standard resistance is generally used in measurement circuits.

????: Difference between ???????? and the impedance angle of ???????? + ????????.

If the presence of the input capacitance ????0 of the amplified input system is not considered,???????? is the measured coating complex impedance ????????, and if the presence of the input capacitance is considered, it is the combined impedance of the coating complex impedance in parallel with the capacitance, satisfying the following relationship

 

????

 ????   =      ????????       ?4?

1+???????? ????0 ????????


The complex impedance of the coating under test is:

 

????

????   =      ????????      ?5?

1−???????? ????0 ????????


Understanding of sine fitting

Simple moving average method

First, we use the simple moving average method to feel the meaning of "moving".

There is a sequence as follows

If a moving average with a window of 5 is used, the element with a sequence of 11 and a value of 2 should be replaced with

????11 = (8 + 5 + 2 + 1 + 3)/5?6?

 

Then the element with a sequence of 12 and a value of 1 should be replaced with

????12 = (5 + 2 + 1 + 3 + 6)/5?7?

 

For fast calculation, the following formula can be used for recursion

????12 = (5 ∗ ????11 + 6 − 8)/5?8?

 

Simple   moving   average   is   defined as: Simple   moving   average of data ????1, ????2, . . ., ???????? with window ????:


The iteration form is:

In MATLAB, there is a corresponding smooth function available. We can use ???????????????????????? to verify smooth (y, span). The following figure shows the result of data 2= smooth (data1,5)

 

Results

In large impedance measurements, the signal is extremely weak, so a differential circuit is introduced to change it into complex impedance form, and the simplicity of sine fitting in amplitude and phase calculation is used to assist in calculating the impedance magnitude, which plays an important role in subsequent large impedance measurements

 

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