# Development of an Online Monitoring Device for the Mixing Ratio of Two-Part Epoxy Adhesives Using an Electrical Impedance Spectroscopy Technique and Machine Learning

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Two-Part Epoxy Adhesive Overview

#### 1.1. The Importance of the Mixing Ratio of Two-Part Epoxy Adhesive at Mixing Process

#### 1.2. Method for Measuring Material Properties Using an Impedance Measurement Technique

#### 1.3. Estimation Method Using Machine Learning

## 2. The Method for the Estimation of the Characteristics for Liquid Materials through Impedance Measurement

#### 2.1. Characteristics of Solutions and Relative Permittivity

_{0}is absolute permittivity. C

_{0}is a capacitance when ε

_{0}is 1 that means vacuum between flat electrode plates.

#### 2.2. Relationship between Relative Permittivity and Impedance

_{0}supplied to the two flat electrode plates, it can be expressed as Equation (2). where V is the output voltage and ω means the angular velocity (rad/sec).

#### 2.3. Impedance Characteristics of the Parallel RC Circuit

#### 2.4. Effects of Parasitic Elements

_{P}

_{1}and R

_{P}

_{2}occur due to cable resistance and contact resistance of connectors [40]. In addition, the parasitic capacitor (C

_{P}) is generated when two wires are long and close to each other. Additionally, parasitic coils (L

_{P}

_{1}, L

_{P}

_{2}) are induced when the cable is twisted. The configuration of a complex circuit network causes many errors, even in the frequency response. Since the parasitic resistance is very small compared to the resistance of the electrode plates at low frequency, the effect is also minimal. However, at a high frequency, the resistance of the electrode plates also becomes small, so it is necessary to be careful. Even if the parasitic capacitor has a constant value, it acts as a capacitance measurement error. The impedance due to the parasitic coil increases according to the frequency increases, causing many errors at high frequency; therefore, if the measurement frequency is carried out in a relatively low-frequency range, the effect of the parasitic elements can be minimized. Therefore, the selection of a moderately low cut-off frequency is advantageous for impedance measurement.

#### 2.5. Connection of Additional Resistor

_{a}(10 kΩ), is connected in parallel with the two flat electrodes.

_{a}is more than 100 times smaller than R at low frequencies and the parallel resistance composed of R and R

_{a}induces more complex non-linear characteristics as shown in Figure 7. For example, when R is 1 MΩ and R

_{a}is 10 kΩ, the total resistance becomes 9.901 kΩ according to the parallel connection formula of resistors, and when it is 10 MΩ, the total resistance becomes 9.90 kΩ. Therefore, it has the effect of changing a change of 1 to 10 MΩ into a change of 89 Ω, so it has non-linearity and is very insensitive to the change of ε″. However, there is an advantage that the cut-off frequency of the impedance equivalent circuit can be adjusted from a high frequency to a low frequency. This has the effect of significantly reducing the error caused by parasitic elements at high frequencies.

## 3. Experimental Device Configuration and Results

#### 3.1. Configuration of the Impedance Measurement Circuit

_{x}(ω)) of varying frequency is input to an unknown RLC network, and the current I(ω) flowing at this time is converted into a voltage V

_{o}(ω) using an I-V converter. It can be applied to a wide range of frequencies from 20 Hz to 120 MHz, and has the advantage of high precision compared to other methods.

^{2}C communication, a component for impedance measurement by Analog Device Inc., was used. It sweeps the input frequency within a specific range, collects the data of the output voltage, and applies the DFT (Discrete Fourier Transform) algorithm to obtain the magnitude and phase difference in the impedance for each frequency.

#### 3.2. Impedance Change According to Temperature Change

^{2}C and SPI communication and execution of machine learning algorithms.

#### 3.3. Design of Sensor Structure for Impedance Measurement

_{0}is 1000 Ω, and resistance tolerance is ±0.12%.

#### 3.4. Composition of Two-Part Epoxy Adhesive Mixing Experiment Equipment

#### 3.5. Experimental Progress and Analysis of Result Data

#### 3.6. Impedance Change with Temperature Change

## 4. Mixing Ratio Estimation Using Machine Learning Algorithm

#### 4.1. Data Preprocessing for Machine Learning

#### 4.2. Training and Evaluation of Machine Learning Models

#### 4.3. A Suggestion for Configuring a Remote Online Monitoring System

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Schematic diagram of a dosing system for two-part epoxy adhesive (modified from [1]).

**Figure 4.**Bode plots of RC parallel circuit: (

**a**) Change in capacitance (R = 10 kΩ); (

**b**) Change in resistance (C = 1 μF).

**Figure 9.**Impedance measurement board with Raspberry Pi: (

**a**) Block diagram; (

**b**) A picture of the developed device.

**Figure 14.**The composition of the experimental device: (

**a**) Fixed ratio two-part epoxy adhesive mixing device with sensor; (

**b**) A picture of the experimental device.

**Figure 15.**Measured impedance graph: (

**a**) Impedance graph by different mixture ratio at 13 °C; (

**b**) Impedance graph by different temperatures.

**Figure 16.**Modified impedance graph and impedance weight graph: (

**a**) Estimated impedance by each frequency; (

**b**) Impedance weight by each frequency.

No. | Test Data | Predicted Ratio (%) | Error (%) | |
---|---|---|---|---|

Temperature (°C) | Ratio (%) | |||

1 | 25.23 | 71.47 | 71.58 | −0.11 |

2 | 25.23 | 36.78 | 37.13 | −0.35 |

3 | 38.88 | 40.87 | 41.03 | −0.16 |

4 | 38.88 | 39.84 | 39.55 | 0.29 |

5 | 19.03 | 72.09 | 72.81 | −0.72 |

6 | 19.03 | 53.15 | 53.09 | 0.06 |

7 | 35.39 | 37.62 | 37.71 | −0.09 |

8 | 35.39 | 29.07 | 28.33 | 0.74 |

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**MDPI and ACS Style**

Choi, J.H.; An, C.H. Development of an Online Monitoring Device for the Mixing Ratio of Two-Part Epoxy Adhesives Using an Electrical Impedance Spectroscopy Technique and Machine Learning. *Processes* **2022**, *10*, 951.
https://doi.org/10.3390/pr10050951

**AMA Style**

Choi JH, An CH. Development of an Online Monitoring Device for the Mixing Ratio of Two-Part Epoxy Adhesives Using an Electrical Impedance Spectroscopy Technique and Machine Learning. *Processes*. 2022; 10(5):951.
https://doi.org/10.3390/pr10050951

**Chicago/Turabian Style**

Choi, Jeong Hee, and Chae Hun An. 2022. "Development of an Online Monitoring Device for the Mixing Ratio of Two-Part Epoxy Adhesives Using an Electrical Impedance Spectroscopy Technique and Machine Learning" *Processes* 10, no. 5: 951.
https://doi.org/10.3390/pr10050951