<p><InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41365_2025_1749_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\beta\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation>-ray-induced X-ray spectroscopy (BIXS) is a promising technique for tritium analysis that offers several unique advantages, including substantial detection depth, nondestructive testing capabilities, and ease of operation. For thin solid tritium-containing samples with substrates, the currently used BIXS analysis method can measure the tritium depth profile and content when the sample thickness is known. In this study, a backpropagation (BP) neural network algorithm was used to predict the tritium content and thickness of a thin solid tritium-containing sample with substrates and a uniformly distributed tritium profile. A semi-analytical method was used to generate datasets for training and testing the BP neural network. A dataset of <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41365_2025_1749_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\beta\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation>-decay X-ray spectra from 420 tritium-containing zirconium models with different known thicknesses and tritium-to-zirconium ratios was used as the input data. The corresponding zirconium thicknesses and tritium-to-zirconium ratios served as the output for training and testing the BP neural network. The mean relative errors (MREs) of the zirconium thickness in the training and test datasets were 0.56% and 0.42%, respectively, whereas the MREs of the tritium-to-zirconium ratio were 0.59% and 0.38%, respectively. Furthermore, the trained BP neural network demonstrates excellent predictive capability across various levels of statistical uncertainty. For the experimental <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41365_2025_1749_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\beta\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation>-decay X-ray spectra of two tritium-containing samples, the predicted zirconium thicknesses and tritium-to-zirconium ratios showed good agreement with the results obtained through the elastic backscattering spectrometry (EBS).</p>

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\(\beta\)-ray induced X-ray spectroscopy for tritium analysis with back propagation neural network

  • Hong Huang,
  • Zhu An,
  • Jing-Jun Zhu

摘要

\(\beta\) β -ray-induced X-ray spectroscopy (BIXS) is a promising technique for tritium analysis that offers several unique advantages, including substantial detection depth, nondestructive testing capabilities, and ease of operation. For thin solid tritium-containing samples with substrates, the currently used BIXS analysis method can measure the tritium depth profile and content when the sample thickness is known. In this study, a backpropagation (BP) neural network algorithm was used to predict the tritium content and thickness of a thin solid tritium-containing sample with substrates and a uniformly distributed tritium profile. A semi-analytical method was used to generate datasets for training and testing the BP neural network. A dataset of \(\beta\) β -decay X-ray spectra from 420 tritium-containing zirconium models with different known thicknesses and tritium-to-zirconium ratios was used as the input data. The corresponding zirconium thicknesses and tritium-to-zirconium ratios served as the output for training and testing the BP neural network. The mean relative errors (MREs) of the zirconium thickness in the training and test datasets were 0.56% and 0.42%, respectively, whereas the MREs of the tritium-to-zirconium ratio were 0.59% and 0.38%, respectively. Furthermore, the trained BP neural network demonstrates excellent predictive capability across various levels of statistical uncertainty. For the experimental \(\beta\) β -decay X-ray spectra of two tritium-containing samples, the predicted zirconium thicknesses and tritium-to-zirconium ratios showed good agreement with the results obtained through the elastic backscattering spectrometry (EBS).