<p>This study focuses on the self-sensing capacity, which is indicated by gauge factor (GF) of strain-hardening fiber-reinforced cementitious composites (SH-FRCCs) for flexural specimen. At first, a machine learning model using a hybrid Random Forest–Particle Swarm Optimization (RF-PSO) technique was proposed to predict the GF for SH-FRCCs under direct tension. After that, an experimental program was conducted to validate the RF-PSO model in predicting GF of SH-FRCCs at the tensile zone of the flexural specimen. A dataset comprising 86 samples gathered from multiple previous studies was utilized to train and evaluate the proposed RF-PSO model. Eight potential input variables were considered: matrix strength (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42107_2025_1291_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="30" /> </InlineMediaObject> <EquationSource Format="TEX">\(\sigma_{mu}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>σ</mi> <mrow> <mi mathvariant="italic">mu</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>), fiber type (FT), fiber geometry (<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42107_2025_1291_Article_IEq2.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="46" /> </InlineMediaObject> <EquationSource Format="TEX">\(L_{f} /d_{f}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>L</mi> <mi>f</mi> </msub> <mo stretchy="false">/</mo> <msub> <mi>d</mi> <mi>f</mi> </msub> </mrow> </math></EquationSource> </InlineEquation>), fiber volume content (<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42107_2025_1291_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(V_{f}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>V</mi> <mi>f</mi> </msub> </math></EquationSource> </InlineEquation>), post-cracking strength (<InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42107_2025_1291_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\(\sigma_{pc}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>σ</mi> <mrow> <mi mathvariant="italic">pc</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>), strain capacity (<InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42107_2025_1291_Article_IEq5.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(\varepsilon_{pc}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>ε</mi> <mrow> <mi mathvariant="italic">pc</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>), initial electrical resistivity (<InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42107_2025_1291_Article_IEq6.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\rho_{i}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>ρ</mi> <mi>i</mi> </msub> </math></EquationSource> </InlineEquation>), electrical resistivity at post cracking (<InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42107_2025_1291_Article_IEq7.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(\rho_{c}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>ρ</mi> <mi>c</mi> </msub> </math></EquationSource> </InlineEquation>). The effectiveness of the hybrid RF-PSO model was assessed via four statistical metrics: R<sup>2</sup> (coefficient of determination), MSE (mean squared error), MAE (mean absolute error), and RMSE (root mean squared error). The analytical results showed that the proposed RF-PSO model showed excellent accuracy, with R<sup>2</sup> values of 0.935 in the training stage and 0.737 in the testing stage. The hybrid RF-PSO model demonstrated superior predictive performance compared to the pure RF model in predicting the GF of SH-FRCCs, improving the R<sup>2</sup> values by 1.05 and 1.14 times in the training and testing stages, respectively. Furthermore, one-dimensional partial dependence plot (PDP-1D) was used to investigate the effect of input variables on the GF of SH-FRCCs. It was found that the <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42107_2025_1291_Article_IEq8.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\(\sigma_{pc}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>σ</mi> <mrow> <mi mathvariant="italic">pc</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42107_2025_1291_Article_IEq9.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(\rho_{c}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>ρ</mi> <mi>c</mi> </msub> </math></EquationSource> </InlineEquation> extremely impacted to the GF predictions. The experimental results showed that the error between the experimental values and RF-PSO predictions is less than -13.63%, thus the proposed model in this study have high generalization capability in predicting the GF of SH-FRCCs.</p>

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Self-sensing capacity of strain-hardening fiber-reinforced cementitious composites: machine learning prediction and experimental validation

  • Duy- Liem Nguyen,
  • Tan-Duy Phan

摘要

This study focuses on the self-sensing capacity, which is indicated by gauge factor (GF) of strain-hardening fiber-reinforced cementitious composites (SH-FRCCs) for flexural specimen. At first, a machine learning model using a hybrid Random Forest–Particle Swarm Optimization (RF-PSO) technique was proposed to predict the GF for SH-FRCCs under direct tension. After that, an experimental program was conducted to validate the RF-PSO model in predicting GF of SH-FRCCs at the tensile zone of the flexural specimen. A dataset comprising 86 samples gathered from multiple previous studies was utilized to train and evaluate the proposed RF-PSO model. Eight potential input variables were considered: matrix strength ( \(\sigma_{mu}\) σ mu ), fiber type (FT), fiber geometry ( \(L_{f} /d_{f}\) L f / d f ), fiber volume content ( \(V_{f}\) V f ), post-cracking strength ( \(\sigma_{pc}\) σ pc ), strain capacity ( \(\varepsilon_{pc}\) ε pc ), initial electrical resistivity ( \(\rho_{i}\) ρ i ), electrical resistivity at post cracking ( \(\rho_{c}\) ρ c ). The effectiveness of the hybrid RF-PSO model was assessed via four statistical metrics: R2 (coefficient of determination), MSE (mean squared error), MAE (mean absolute error), and RMSE (root mean squared error). The analytical results showed that the proposed RF-PSO model showed excellent accuracy, with R2 values of 0.935 in the training stage and 0.737 in the testing stage. The hybrid RF-PSO model demonstrated superior predictive performance compared to the pure RF model in predicting the GF of SH-FRCCs, improving the R2 values by 1.05 and 1.14 times in the training and testing stages, respectively. Furthermore, one-dimensional partial dependence plot (PDP-1D) was used to investigate the effect of input variables on the GF of SH-FRCCs. It was found that the \(\sigma_{pc}\) σ pc and \(\rho_{c}\) ρ c extremely impacted to the GF predictions. The experimental results showed that the error between the experimental values and RF-PSO predictions is less than -13.63%, thus the proposed model in this study have high generalization capability in predicting the GF of SH-FRCCs.