# A Quantitative Ultrasonic Travel-Time Tomography to Investigate Liquid Elaborations in Industrial Processes

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## Abstract

**:**

## 1. Introduction

## 2. Transmission Forward Model

## 3. Sensitivity Matrix Analysis

## 4. Inverse Problem

## 5. System Design—Measurement Data

#### 5.1. TOF Data Acquisition

#### 5.2. Filtering Method

## 6. Experimental Results

#### 6.1. Qualitative Resolution Experiments

#### 6.2. Quantitative Resolution Experiments

^{3}between the inclusion and the medium. The fact that the developed system can respond so accurately to such challenging changes is very optimistic. Moreover, multiple reconstructions with different concentrations proved a great efficiency of the system to distinguish liquids of density differences up to 40 kg/m

^{3}, which is assured by the different results between the 50% and 42.86% solutions.

^{3}, such as in the case of 56.52% concentration, the calculated sound velocity value is not perfectly matching the expected one, according to the trajectory of the relative graph. These quantitative results prove great feasibility and efficiency of USCT in characterizing different densities of liquid solutions.

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Setup of a ring of 32 ultrasonic transducers in a fan beam architecture. (

**a**) One actuated transmitter. (

**b**) Measurement’s principle of a 32-electrode USCT system.

**Figure 2.**

**Left**: Sensitivity maps depicting the different form of ray in each method.

**Middle**: Full frames of sensitivity matrices produced by all the proposed methods for 150 degrees of angle of the beam.

**Right**: Full frames of sensitivity matrices produced by all the proposed methods for 90 degrees of angle of the beam.

**Figure 3.**(

**a**) Singular Values of all the different methods of the sensitivity matrices. It helps to characterize inverse problems according to their ill-posedness. (

**b**) Plots of synthetics data produced by all the different methods of sensitivity matrices against the background measurement.

**Figure 4.**The developed ultrasonic system. A ring of 32 piezoelectric transducers mounted to the black bucket.

**Figure 6.**(

**a**) Display of transmitted, received, and filtered pulse of a single measuring frame. (

**b**) Three possible ways of receiving information by the propagation of the waves. The circular perimeter displays the tank and the dark blue circle inside it displays the object. The form of a received signal.

**Figure 7.**(

**a**) Filtering the raw time-of-flight (TOF) data with the statistical method of “deleting outliers” introduced by F. E. Grubbs [35]. (

**b**) Reconstruction using a single-step linear back-projection algorithm (LBP) with and without filtering the data.

**Figure 8.**(

**a**) Objects used as inclusions in the experiments. (

**b**)

**Left**: True positions of inclusions.

**Middle**: Isotropic total variation reconstruction using a 90 degrees angle beam.

**Right**: Position error in mm.

**Figure 9.**

**Left**: Reconstruction of a moving object in 99 locations within the region of imaging in every 10 frames.

**Right**: Trajectory of the movement of the sample with shape reconstructed with time (Z axis is time).

**Figure 10.**(

**a**) Experimental setup. (

**b**) Experiment with a slurry mixture of sucrose/water. The scale of reconstructions is in sound-speed units (m/s).

**Figure 11.**Graph of concentrations values. Experimental values are represented with black dots and single measurement values form literature studies represented with blue dots. Literature values extracted from Resa et al. study [16].

Numerical Table of Experiments | |||
---|---|---|---|

Mass Concentration Background—Full Measurements | Density | Single TOF Measurements (1-16 Transducer) | Scale of Reconstruction (Velocity) |

0% gr/mL | 995.3 (kg/m^{3}) | 162 μs | - |

20% gr/mL | 1075 (kg/m^{3}) | 161 μs | 1480–1513.93 m/s |

33% gr/mL | 1134 (kg/m^{3}) | 159 μs | 1480–1577.31 m/s |

42.86% gr/mL | 1184 (kg/m^{3}) | 158 μs | 1480–1617.65 m/s |

50% gr/mL | 1224 (kg/m^{3}) | 157 μs | 1480–1660.87 m/s |

56.52% gr/mL | 1259 (kg/m^{3}) | 157 μs | 1480–1661.51 m/s |

60.78% gr/mL | 1284 (kg/m^{3}) | 156 μs | 1480–1755.86 m/s |

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**MDPI and ACS Style**

Koulountzios, P.; Rymarczyk, T.; Soleimani, M.
A Quantitative Ultrasonic Travel-Time Tomography to Investigate Liquid Elaborations in Industrial Processes. *Sensors* **2019**, *19*, 5117.
https://doi.org/10.3390/s19235117

**AMA Style**

Koulountzios P, Rymarczyk T, Soleimani M.
A Quantitative Ultrasonic Travel-Time Tomography to Investigate Liquid Elaborations in Industrial Processes. *Sensors*. 2019; 19(23):5117.
https://doi.org/10.3390/s19235117

**Chicago/Turabian Style**

Koulountzios, Panagiotis, Tomasz Rymarczyk, and Manuchehr Soleimani.
2019. "A Quantitative Ultrasonic Travel-Time Tomography to Investigate Liquid Elaborations in Industrial Processes" *Sensors* 19, no. 23: 5117.
https://doi.org/10.3390/s19235117