# Conductor Identification Using Acoustic Signal Method

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}and 25 mm

^{2}, respectively) and 0.22% between conductors with polyethylene and PVC insulations. The prototype of conductor identification device was assembled in a way that practically confirmed the theoretical research with the average percentage of discrepancy of about 1.44%. In addition, the paper analyzes the conductor identification operation constituents to justify the application of the acoustic method by comparison with other identification methods.

## 1. Introduction

#### 1.1. Existing Methods for Identifying Conductors

#### 1.2. Hypothesis of Using Acoustic Signal for Identifying Conductors

#### 1.3. Article Contribution and Organization

## 2. Acoustic Method for Identifying Conductors

## 3. Mathematical Modeling of Sound Propagation in Conductors and Insulation

- 1.
- To set the initial data such as the length of a conductor (distance from identification point to sound source), the frequency of the supplied signal, the cross-section of the conductor as well as the sound pressure level of the sound source ${P}_{dB}$, dB.
- 2.
- To determine the wavelength of acoustic waves $\lambda $, m:$$\lambda =\frac{V}{f}$$$V$ is the propagation velocity of acoustic waves, m/s;$f$ is frequency of acoustic waves, Hz;
- 3.
- To determine the propagation constant $k$, m
^{−1}:$$k=\frac{2\pi}{\mathsf{\lambda}}$$ - 4.
- To determine force $F$, N, applied to a conductor by a vibrational speaker:$$F=P\xb7{S}_{c}$$$P$ is the mechanical stress, N/m
^{2}, Pa;${S}_{c}$ is the contact area between a conductor and a vibrational speaker, m^{2}. - 5.
- To determine the absolute elongation of a conductor $\Delta l$, m:$$\Delta l=\frac{F\xb7l}{A\xb7E}$$$F$ is applied force, N;$l$ is conductor length, m;$A$ is conductor cross-section, m
^{2};$E$ is modulus of material elasticity, N/m^{2}. - 6.
- To determine the relative length of the conductor after the absolute elongation ${l}_{rel}$, m:$${l}_{rel}=\Delta l+l$$$l$ is conductor length, m.
- 7.
- To determine the conductor deformation $S$, dimensionless number (DN):$$S={l}_{rel}/\lambda $$${l}_{rel}$ is the relative length of the conductor, m;$\lambda $ is the wavelength of acoustic waves, m.
- 8.
- To determine the displacement amplitude of conductor particles ${u}_{m}$, m:$${u}_{m}=\frac{S}{k}$$$S$ is conductor deformation, DN;$k$ is the propagation constant, m
^{−1}. - 9.
- To determine the vibration velocity in a conductor V, m/s:$$V=2\pi f{u}_{m}$$$f$ is the frequency of the acoustic signal, Hz;${u}_{m}$is displacement amplitude of conductor particles, m.
- 10.
- To determine the reflection coefficient at the interface between two media (conductive core-conductor insulation), ${R}_{ref}$, DN:$${R}_{ref}=\frac{{Z}_{core}-{Z}_{insul}}{{Z}_{core}+{Z}_{insul}}$$${Z}_{core}$ is the acoustic resistance of the conductor core, kg/(m
^{2}·s);${Z}_{insul}$ is the acoustic resistance of the conductor insulation, kg/(m^{2}·s).The acoustic resistance of conductor core ${Z}_{core}$, kg/(m^{2}·s), is calculated as follows:$${Z}_{core}={V}_{sound.core}\xb7{\rho}_{0.core}$$${V}_{sound.core}$ is longitudinal wave velocity in a conductor core, m/s;${\rho}_{0.core}$ is the density of conductor core material, kg/m^{3}. - 11.
- To determine the loss coefficient of sound wave energy transition into other energy types (in particular into heat) ${R}_{loss}$, DN:$${R}_{loss}=\frac{\alpha \xb7\left(\lambda \xb7100\right)}{\pi}$$α is the sound absorption coefficient, cm
^{−1};λ is the wavelength of the acoustic waves, m.The values of the sound absorption coefficient are usually written in measurement units of dB/сm. According to [26], α equals to 2.44 × 10^{−4}dB/cm for copper and 3.15 × 10^{−4}dB/cm for aluminum. In order to convert units from dB/cm to 1/cm, it is necessary to use the following equation:$$\alpha \left[1/\mathrm{cm}\right]=\frac{\alpha \left[\mathrm{dB}/\mathrm{cm}\right]}{20\mathrm{lg}\left(e\right)}=\frac{\alpha \left[\mathrm{dB}/\mathrm{cm}\right]}{8686}$$ - 12.
- To determine the sound pressure level at the identification point ${L}_{p}$, dB:$${L}_{p}={P}_{dB}-10\mathrm{lg}\frac{{V}^{2}}{{V}_{0}^{2}}\xb7{R}_{ref}\xb7{R}_{loss}={P}_{dB}-20\mathrm{lg}\left(\frac{V}{{V}_{0}}\right)\xb7{R}_{ref}\xb7{R}_{loss}$$$V$ is vibration velocity in a conductor, m/s;${V}_{0}=5\times {10}^{-8}$ is the reference value of vibration velocity, m/s;${P}_{\mathrm{dB}}$ is the sound pressure level of the sound source, dB;${R}_{ref}$ is the reflection coefficient at the interface between two media, DN;${R}_{loss}$ is the loss coefficient, DN.

^{2}, the sound pressure level at a distance (from the identification point to the signal source) of 100 m turned out to be only 3.65% (0.85 dB) less than at a distance of 5 m.

^{2}. Therefore, the difference in sound pressure level at the minimum and maximum cross sections was approximately 0.07 dB, that is 0.42%.

^{2}and with PVC insulation will be 7.2 dB at the distance of 30 m from the sound source while it will be 7.55 dB at the distance of 100 m. Therefore, the change in level losses at the distances of 30 m and 100 m is just 0.35 dB, that is, 4.64%.

## 4. Functional Testing of Acoustic Method

#### 4.1. Prototype of Conductor Identification Device

#### 4.2. Multivariate Experiment to Test Acoustic Method for Conductor Identification

^{2}was used in the comparison. The level of source sound pressure supplied to the conductor was 30 dB, the frequency of the applied signal was 80 Hz. Control points along conductor length were chosen 5, 10, 15 and 20 m.

## 5. Analyses of Conductor Identification Operation Duration

^{2}was used as a control sample of the wiring, internal and external insulation of which are made of polyvinyl chloride. The number of experiment repetitions for each operation was 10.

^{2}and laid openly on brick and concrete foundations.

## 6. Conclusions

^{2}and 25 mm

^{2}, respectively) is insignificant and amounts to 0.07 dB. Likewise, the insulation type of conductors also has a negligible effect on sound propagation.

## 7. Patents

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Block diagram of the implementation of the acoustic method for identifying conductors: (ASG) Acoustic signal generator; (VS) Vibrational speaker; (PS) Piezoelectric sensor; (ASR) Acoustic signal receiver; (CI) Conductor insulation; (CC) Conductor core; (АS) Acoustic signal; (CW) Connecting wire.

**Figure 2.**Graphs of theoretical calculations of the sound pressure level in conductors: (

**a**) Sound pressure level in copper conductors with a cross section of 2.5 mm

^{2}with PVC insulation and polyethylene insulation, depending on the length of the conductor; (

**b**) Sound pressure level in a copper conductor 5 m long, depending on the cross section of conductor.

**Figure 3.**Block diagram of the conductor identification device on the basis of acoustic method: (ASG) Acoustic signal generator; (VS) Vibrational speaker; (PS) Piezoelectric sensor; (ASR) Acoustic signal receiver; (AB) Accumulator battery.

**Figure 4.**Appearance of СID prototype: (ASG) Acoustic signal generator; (ASR) Acoustic signal receiver.

**Figure 5.**Diagram of the experiment to test the acoustic method for conductor identification: (ASG) Acoustic signal generator; (VS) Vibrational speaker; (PS) Piezoelectric sensor; (ASR) Acoustic signal receiver; (IC) Identifiable conductor; (AC) adjacent Conductor; (СI) Conductor insulation.

**Figure 6.**Response surfaces of the sound pressure level in conductors: (

**a**) Theoretical dependence; (

**b**) Practical (experimental) dependence.

**Figure 7.**Comparison of theoretical and practical data in terms of sound pressure level dependence on conductor length.

Name of Component | Quantity | Unit Price, US$ | Amount, US$ |
---|---|---|---|

Vibrational speaker | 2 | 2 | 4 |

Signal amplifier PAM8610 | 1 | 6 | 6 |

Bluetooth audio signal playback module | 1 | 5 | 5 |

Power supply module | 2 | 4 | 8 |

Piezoelectric sensor | 1 | 12 | 12 |

Signal amplifier NE5532 | 1 | 6 | 6 |

Sound level indicator module | 1 | 6 | 6 |

Rechargeable lithium battery 3.7 V 3400 mAh | 6 | 10 | 60 |

Charger DC 12V 2A | 1 | 11 | 11 |

Plastic housing | 2 | 12 | 24 |

Total: | 142 |

Conductor Cross Section | $\mathit{k}$ |
---|---|

Internal power networks laid openly on brick and concrete foundations | |

from 1.5 to 6 | 1 |

from 6 to 25 | 1.05 |

from 25 to 35 | 1.1 |

from 35 to 70 | 1.3 |

from 70 and more | 1.48 |

Internal power networks laid hidden | |

from 1.5 to 6 | 1.1 |

from 6 to 25 | 1.22 |

from 25 to 35 | 1.31 |

from 35 to 70 | 1.43 |

from 70 and more | 1.7 |

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**MDPI and ACS Style**

Bukreev, A.; Vinogradov, A.; Bolshev, V.; Panchenko, V.
Conductor Identification Using Acoustic Signal Method. *Sustainability* **2022**, *14*, 7297.
https://doi.org/10.3390/su14127297

**AMA Style**

Bukreev A, Vinogradov A, Bolshev V, Panchenko V.
Conductor Identification Using Acoustic Signal Method. *Sustainability*. 2022; 14(12):7297.
https://doi.org/10.3390/su14127297

**Chicago/Turabian Style**

Bukreev, Alexey, Alexander Vinogradov, Vadim Bolshev, and Vladimir Panchenko.
2022. "Conductor Identification Using Acoustic Signal Method" *Sustainability* 14, no. 12: 7297.
https://doi.org/10.3390/su14127297