<p>Acoustic emission (AE) sensor array plays a crucial role in laboratory rock mechanics experiments. Most research studies rely on empirically designed sensor arrays, such as those evenly deployed across the monitored targets. While those arrangements may suffice for source localization, but may be inadequate for moment-tensor inversion as the poor sensor coverage may lead to significant uncertainty and non-uniqueness in source mechanisms. To enhance sensor coverage, we present a quantitative method for optimizing sensor arrangement by maximizing the uniform distribution of points on a unit sphere, formulated based on the Tammes problem. We first maximize the angular distance between sensors placed on a unit sphere. We then determine the sensors’ actual locations on the sample surface by projecting them from the unit sphere onto the sample. Furthermore, we assess the enhancement in sensor coverage resulting from the sensor array optimization by calculating and examining the spatial distribution of the condition numbers for moment-tensor inversions of sources on both observed and forecasted fracture planes. It can be shown that some empirically deployed sensor arrays may exhibit limited angular coverage in regions where AE events are intensively occurring, such as the center of the sample. In contrast, the optimized sensor arrays may notably enhance sensor coverage in regions rich with events, showing the reduction in condition number of up to <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="603_2025_4605_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">\(99.89\%\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>99.89</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="603_2025_4605_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="43" /> </InlineMediaObject> <EquationSource Format="TEX">\(89.4\%\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>89.4</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation>, and <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="603_2025_4605_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">\(61.27\%\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>61.27</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> in our examples. Therefore, future AE laboratory experiments could greatly benefit from the optimization of sensor arrangements.</p>

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Quantitative Optimization of Sensor Positions in Laboratory Acoustic Emission Experiments

  • Liang Ding,
  • Gang Yang,
  • Edouard Kravchinsky,
  • Afeez K. Popoola,
  • Sebastian D. Goodfellow,
  • Qinya Liu,
  • Giovanni Grasselli

摘要

Acoustic emission (AE) sensor array plays a crucial role in laboratory rock mechanics experiments. Most research studies rely on empirically designed sensor arrays, such as those evenly deployed across the monitored targets. While those arrangements may suffice for source localization, but may be inadequate for moment-tensor inversion as the poor sensor coverage may lead to significant uncertainty and non-uniqueness in source mechanisms. To enhance sensor coverage, we present a quantitative method for optimizing sensor arrangement by maximizing the uniform distribution of points on a unit sphere, formulated based on the Tammes problem. We first maximize the angular distance between sensors placed on a unit sphere. We then determine the sensors’ actual locations on the sample surface by projecting them from the unit sphere onto the sample. Furthermore, we assess the enhancement in sensor coverage resulting from the sensor array optimization by calculating and examining the spatial distribution of the condition numbers for moment-tensor inversions of sources on both observed and forecasted fracture planes. It can be shown that some empirically deployed sensor arrays may exhibit limited angular coverage in regions where AE events are intensively occurring, such as the center of the sample. In contrast, the optimized sensor arrays may notably enhance sensor coverage in regions rich with events, showing the reduction in condition number of up to \(99.89\%\) 99.89 % , \(89.4\%\) 89.4 % , and \(61.27\%\) 61.27 % in our examples. Therefore, future AE laboratory experiments could greatly benefit from the optimization of sensor arrangements.