Detection of Background Water Leaks Using a High-Resolution Dyadic Transform
This article solves the problem of detecting water leaks with a minimum size of down to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mrow><mtext> </mtext><mi&...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-02-01
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| Series: | Water |
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| Online Access: | https://www.mdpi.com/2073-4441/15/4/736 |
| _version_ | 1797617710729789440 |
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| author | Eduardo Trutié-Carrero Diego Seuret-Jiménez José M. Nieto-Jalil Julio C. Herrera-Díaz Jorge Cantó J. Jesús Escobedo-Alatorre |
| author_facet | Eduardo Trutié-Carrero Diego Seuret-Jiménez José M. Nieto-Jalil Julio C. Herrera-Díaz Jorge Cantó J. Jesús Escobedo-Alatorre |
| author_sort | Eduardo Trutié-Carrero |
| collection | DOAJ |
| description | This article solves the problem of detecting water leaks with a minimum size of down to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mrow><mtext> </mtext><mi>mm</mi></mrow></mrow></semantics></math></inline-formula> in diameter. Two new mathematical tools are used to solve this problem: the first one is the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">T</mi><mi>e</mi></msub></mrow></semantics></math></inline-formula> cross-spectral density and the second is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">T</mi><mi>e</mi></msub></mrow></semantics></math></inline-formula> coherence. These mathematical tools provide the possibility of discriminating spurious frequency components, making use of the property of multi-sensitivity. This advantage makes it possible to maximize the sensitivity of the frequency spectrum. The wavelet function used was Daubechies <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>45</mn></mrow></semantics></math></inline-formula>, because it provides an attenuation of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>150</mn><mrow><mtext> </mtext><mi>dB</mi></mrow></mrow></semantics></math></inline-formula> in the rejection band. The tools were validated with two scenarios. For the first scenario, a synthetic signal was analyzed. In the second scenario, two types of background leakage were analyzed: the first one has a diameter of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mrow><mtext> </mtext><mi>mm</mi></mrow></mrow></semantics></math></inline-formula> with a signal-to-noise ratio of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2.82</mn><mrow><mtext> </mtext><mi>dB</mi></mrow></mrow></semantics></math></inline-formula> and flow rate of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>33.7</mn><mrow><mtext> </mtext><mi>mL</mi></mrow><mo>/</mo><mi mathvariant="normal">s</mi></mrow></semantics></math></inline-formula>, and the second one has a diameter of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>4</mn><mrow><mtext> </mtext><mi>mm</mi></mrow></mrow></semantics></math></inline-formula> with a signal-to-noise ratio of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>9.73</mn><mrow><mtext> </mtext><mi>dB</mi></mrow></mrow></semantics></math></inline-formula> with a flow rate of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>125.0</mn><mrow><mtext> </mtext><mi>mL</mi></mrow><mo>/</mo><mi mathvariant="normal">s</mi></mrow></semantics></math></inline-formula>. The results reported in this paper show that both the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">T</mi><mi>e</mi></msub></mrow></semantics></math></inline-formula> cross-spectral density and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">T</mi><mi>e</mi></msub></mrow></semantics></math></inline-formula> coherence are higher than those reported in scientific literature. |
| first_indexed | 2024-03-11T07:59:41Z |
| format | Article |
| id | doaj.art-623d18f11ddd4598b3ca8241ba2ffb12 |
| institution | Directory Open Access Journal |
| issn | 2073-4441 |
| language | English |
| last_indexed | 2024-03-11T07:59:41Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Water |
| spelling | doaj.art-623d18f11ddd4598b3ca8241ba2ffb122023-11-16T23:52:47ZengMDPI AGWater2073-44412023-02-0115473610.3390/w15040736Detection of Background Water Leaks Using a High-Resolution Dyadic TransformEduardo Trutié-Carrero0Diego Seuret-Jiménez1José M. Nieto-Jalil2Julio C. Herrera-Díaz3Jorge Cantó4J. Jesús Escobedo-Alatorre5Centro de Investigación en Ingeniería y Ciencias Aplicadas, Universidad Autónoma del Estado de Morelos, Ave. Universidad 1001, Cuernavaca 62209, MexicoCentro de Investigación en Ingeniería y Ciencias Aplicadas, Universidad Autónoma del Estado de Morelos, Ave. Universidad 1001, Cuernavaca 62209, MexicoTecnologico de Monterrey, School of Engineering and Sciences, Reserva Territorial Atlixcáyotl, Puebla 72453, MexicoCentro de Investigación en Ingeniería y Ciencias Aplicadas, Universidad Autónoma del Estado de Morelos, Ave. Universidad 1001, Cuernavaca 62209, MexicoCorrosión y Protección (CyP), Buffon 46, Mexico City 11590, MexicoCentro de Investigación en Ingeniería y Ciencias Aplicadas, Universidad Autónoma del Estado de Morelos, Ave. Universidad 1001, Cuernavaca 62209, MexicoThis article solves the problem of detecting water leaks with a minimum size of down to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mrow><mtext> </mtext><mi>mm</mi></mrow></mrow></semantics></math></inline-formula> in diameter. Two new mathematical tools are used to solve this problem: the first one is the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">T</mi><mi>e</mi></msub></mrow></semantics></math></inline-formula> cross-spectral density and the second is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">T</mi><mi>e</mi></msub></mrow></semantics></math></inline-formula> coherence. These mathematical tools provide the possibility of discriminating spurious frequency components, making use of the property of multi-sensitivity. This advantage makes it possible to maximize the sensitivity of the frequency spectrum. The wavelet function used was Daubechies <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>45</mn></mrow></semantics></math></inline-formula>, because it provides an attenuation of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>150</mn><mrow><mtext> </mtext><mi>dB</mi></mrow></mrow></semantics></math></inline-formula> in the rejection band. The tools were validated with two scenarios. For the first scenario, a synthetic signal was analyzed. In the second scenario, two types of background leakage were analyzed: the first one has a diameter of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mrow><mtext> </mtext><mi>mm</mi></mrow></mrow></semantics></math></inline-formula> with a signal-to-noise ratio of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2.82</mn><mrow><mtext> </mtext><mi>dB</mi></mrow></mrow></semantics></math></inline-formula> and flow rate of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>33.7</mn><mrow><mtext> </mtext><mi>mL</mi></mrow><mo>/</mo><mi mathvariant="normal">s</mi></mrow></semantics></math></inline-formula>, and the second one has a diameter of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>4</mn><mrow><mtext> </mtext><mi>mm</mi></mrow></mrow></semantics></math></inline-formula> with a signal-to-noise ratio of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>9.73</mn><mrow><mtext> </mtext><mi>dB</mi></mrow></mrow></semantics></math></inline-formula> with a flow rate of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>125.0</mn><mrow><mtext> </mtext><mi>mL</mi></mrow><mo>/</mo><mi mathvariant="normal">s</mi></mrow></semantics></math></inline-formula>. The results reported in this paper show that both the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">T</mi><mi>e</mi></msub></mrow></semantics></math></inline-formula> cross-spectral density and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">T</mi><mi>e</mi></msub></mrow></semantics></math></inline-formula> coherence are higher than those reported in scientific literature.https://www.mdpi.com/2073-4441/15/4/736cross-correlationfrequency dyadic spectrum<named-content content-type="inline"><inline-formula> <mml:math id="mm111113"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi mathvariant="script">T</mml:mi> <mml:mi>e</mml:mi> </mml:msub> </mml:mrow> </mml:semantics> </mml:math> </inline-formula></named-content> coherence<named-content content-type="inline"><inline-formula> <mml:math id="mm111114"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi mathvariant="script">T</mml:mi> <mml:mi>e</mml:mi> </mml:msub> </mml:mrow> </mml:semantics> </mml:math> </inline-formula></named-content> cross-spectral density<named-content content-type="inline"><inline-formula> <mml:math id="mm111115"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi mathvariant="script">T</mml:mi> <mml:mi>e</mml:mi> </mml:msub> </mml:mrow> </mml:semantics> </mml:math> </inline-formula></named-content> transform |
| spellingShingle | Eduardo Trutié-Carrero Diego Seuret-Jiménez José M. Nieto-Jalil Julio C. Herrera-Díaz Jorge Cantó J. Jesús Escobedo-Alatorre Detection of Background Water Leaks Using a High-Resolution Dyadic Transform Water cross-correlation frequency dyadic spectrum <named-content content-type="inline"><inline-formula> <mml:math id="mm111113"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi mathvariant="script">T</mml:mi> <mml:mi>e</mml:mi> </mml:msub> </mml:mrow> </mml:semantics> </mml:math> </inline-formula></named-content> coherence <named-content content-type="inline"><inline-formula> <mml:math id="mm111114"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi mathvariant="script">T</mml:mi> <mml:mi>e</mml:mi> </mml:msub> </mml:mrow> </mml:semantics> </mml:math> </inline-formula></named-content> cross-spectral density <named-content content-type="inline"><inline-formula> <mml:math id="mm111115"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi mathvariant="script">T</mml:mi> <mml:mi>e</mml:mi> </mml:msub> </mml:mrow> </mml:semantics> </mml:math> </inline-formula></named-content> transform |
| title | Detection of Background Water Leaks Using a High-Resolution Dyadic Transform |
| title_full | Detection of Background Water Leaks Using a High-Resolution Dyadic Transform |
| title_fullStr | Detection of Background Water Leaks Using a High-Resolution Dyadic Transform |
| title_full_unstemmed | Detection of Background Water Leaks Using a High-Resolution Dyadic Transform |
| title_short | Detection of Background Water Leaks Using a High-Resolution Dyadic Transform |
| title_sort | detection of background water leaks using a high resolution dyadic transform |
| topic | cross-correlation frequency dyadic spectrum <named-content content-type="inline"><inline-formula> <mml:math id="mm111113"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi mathvariant="script">T</mml:mi> <mml:mi>e</mml:mi> </mml:msub> </mml:mrow> </mml:semantics> </mml:math> </inline-formula></named-content> coherence <named-content content-type="inline"><inline-formula> <mml:math id="mm111114"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi mathvariant="script">T</mml:mi> <mml:mi>e</mml:mi> </mml:msub> </mml:mrow> </mml:semantics> </mml:math> </inline-formula></named-content> cross-spectral density <named-content content-type="inline"><inline-formula> <mml:math id="mm111115"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi mathvariant="script">T</mml:mi> <mml:mi>e</mml:mi> </mml:msub> </mml:mrow> </mml:semantics> </mml:math> </inline-formula></named-content> transform |
| url | https://www.mdpi.com/2073-4441/15/4/736 |
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