<p>High-temperature shape memory alloys (HTSMA) have strong potential for applications requiring shape memory effects at elevated temperatures. Particularly above 700&#xa0;°C, Ti-based HTSMA has been researched for its higher transformation temperature and mechanical strength. However, the expensive, complex nature of alloy-making and experimental procedures makes research challenging. This study explores the ability of machine learning (ML) models to predict the phase transformation temperature (PTT), i.e., austenite finish (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11665_2025_11236_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(A_{{\text{f}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>A</mi> <mtext>f</mtext> </msub> </math></EquationSource> </InlineEquation>) and martensite start (<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11665_2025_11236_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\(M_{{\text{s}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>M</mi> <mtext>s</mtext> </msub> </math></EquationSource> </InlineEquation>) temperature in NiTi-based HTSMA. Also, thermal hysteresis (<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11665_2025_11236_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="36" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Delta T_{{{\text{th}}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mi>T</mi> <mtext>th</mtext> </msub> </mrow> </math></EquationSource> </InlineEquation>) was calculated using a predicted <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11665_2025_11236_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(A_{{\text{f}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>A</mi> <mtext>f</mtext> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11665_2025_11236_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\(M_{{\text{s}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>M</mi> <mtext>s</mtext> </msub> </math></EquationSource> </InlineEquation> and compared calculated <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11665_2025_11236_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="36" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Delta T_{{{\text{th}}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mi>T</mi> <mtext>th</mtext> </msub> </mrow> </math></EquationSource> </InlineEquation> with actual <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11665_2025_11236_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="36" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Delta T_{{{\text{th}}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mi>T</mi> <mtext>th</mtext> </msub> </mrow> </math></EquationSource> </InlineEquation>, which would help develop HTSMA. This study compares the performance of three ML algorithms: artificial neural network (ANN), support vector regression (SVR), and random forest regression (RFR). ANN performed better in predicting the <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11665_2025_11236_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(A_{{\text{f}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>A</mi> <mtext>f</mtext> </msub> </math></EquationSource> </InlineEquation>, whereas SVR predicted the <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11665_2025_11236_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\(M_{{\text{s}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>M</mi> <mtext>s</mtext> </msub> </math></EquationSource> </InlineEquation> with a higher coefficient of determination (<InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11665_2025_11236_Article_IEq10.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(R^{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>R</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>), minimum root mean square error (RMSE), and mean absolute error (MAE) on unseen data. ANN and SVR identify platinum (Pt) as the most significant element influencing the PTT, whereas RFR captured Ni as the significant element. Interestingly, RFR predicted the <InlineEquation ID="IEq11"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11665_2025_11236_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="36" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Delta T_{{{\text{th}}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mi>T</mi> <mtext>th</mtext> </msub> </mrow> </math></EquationSource> </InlineEquation> calculated from predicted transformation temperatures with the least error and consistently captured the trend in <InlineEquation ID="IEq12"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11665_2025_11236_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="36" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Delta T_{{{\text{th}}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mi>T</mi> <mtext>th</mtext> </msub> </mrow> </math></EquationSource> </InlineEquation> for each element, which was aligned with previous research. This study suggests that ANN and SVR excel in capturing the complex relationship between the input composition and output PTTs, <InlineEquation ID="IEq13"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11665_2025_11236_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(A_{{\text{f}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>A</mi> <mtext>f</mtext> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq14"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11665_2025_11236_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\(M_{{\text{s}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>M</mi> <mtext>s</mtext> </msub> </math></EquationSource> </InlineEquation>, respectively, while RFR predicted the <InlineEquation ID="IEq15"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11665_2025_11236_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="36" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Delta T_{{{\text{th}}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mi>T</mi> <mtext>th</mtext> </msub> </mrow> </math></EquationSource> </InlineEquation> with the least error. Overall, this study could be utilized to accelerate the Ti-based HTSMA design with rapid prediction relevant to temperature-induced behavior for specific applications.</p>

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Machine Learning-Based Temperature-Induced Phase Transformation Temperature Prediction of Ti-Based High-Temperature Shape Memory Alloy

  • S. Sridharan,
  • Ramamoorthy Velayutham,
  • Sudhir Behera,
  • Jayaprakash Murugesan

摘要

High-temperature shape memory alloys (HTSMA) have strong potential for applications requiring shape memory effects at elevated temperatures. Particularly above 700 °C, Ti-based HTSMA has been researched for its higher transformation temperature and mechanical strength. However, the expensive, complex nature of alloy-making and experimental procedures makes research challenging. This study explores the ability of machine learning (ML) models to predict the phase transformation temperature (PTT), i.e., austenite finish ( \(A_{{\text{f}}}\) A f ) and martensite start ( \(M_{{\text{s}}}\) M s ) temperature in NiTi-based HTSMA. Also, thermal hysteresis ( \(\Delta T_{{{\text{th}}}}\) Δ T th ) was calculated using a predicted \(A_{{\text{f}}}\) A f and \(M_{{\text{s}}}\) M s and compared calculated \(\Delta T_{{{\text{th}}}}\) Δ T th with actual \(\Delta T_{{{\text{th}}}}\) Δ T th , which would help develop HTSMA. This study compares the performance of three ML algorithms: artificial neural network (ANN), support vector regression (SVR), and random forest regression (RFR). ANN performed better in predicting the \(A_{{\text{f}}}\) A f , whereas SVR predicted the \(M_{{\text{s}}}\) M s with a higher coefficient of determination ( \(R^{2}\) R 2 ), minimum root mean square error (RMSE), and mean absolute error (MAE) on unseen data. ANN and SVR identify platinum (Pt) as the most significant element influencing the PTT, whereas RFR captured Ni as the significant element. Interestingly, RFR predicted the \(\Delta T_{{{\text{th}}}}\) Δ T th calculated from predicted transformation temperatures with the least error and consistently captured the trend in \(\Delta T_{{{\text{th}}}}\) Δ T th for each element, which was aligned with previous research. This study suggests that ANN and SVR excel in capturing the complex relationship between the input composition and output PTTs, \(A_{{\text{f}}}\) A f and \(M_{{\text{s}}}\) M s , respectively, while RFR predicted the \(\Delta T_{{{\text{th}}}}\) Δ T th with the least error. Overall, this study could be utilized to accelerate the Ti-based HTSMA design with rapid prediction relevant to temperature-induced behavior for specific applications.