<?xml version="1.1" encoding="utf-8"?>
<article xsi:noNamespaceSchemaLocation="http://jats.nlm.nih.gov/publishing/1.1/xsd/JATS-journalpublishing1-mathml3.xsd" dtd-version="1.1" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"><front><journal-meta><journal-id journal-id-type="publisher-id">ME</journal-id><journal-title-group><journal-title>Modern Engineering</journal-title></journal-title-group><issn>2996-6973</issn><eissn>2996-6981</eissn><publisher><publisher-name>Art and Technology</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.61369/ME.2026040037</article-id><article-categories><subj-group subj-group-type="heading"><subject>Article</subject></subj-group></article-categories><title>基于TCN-Transformer的Q195钢应力-应变曲线预测</title><url>https://artdesignp.com/journal/ME/3/4/10.61369/ME.2026040037</url><author>柯贤伦,孟政臣,罗毅恒</author><pub-date pub-type="publication-year"><year>2026</year></pub-date><volume>3</volume><issue>4</issue><history><date date-type="pub"><published-time>2026-04-20</published-time></date></history><abstract>应力-应变曲线是金属板材成形仿真、工艺参数设计和成形质量评价的重要基础，Q195钢在不同加载速率下呈现非线性强化特征。传统Johnson-Cook（J-C）模型形式简洁，但在室温小样本条件下难以充分描述弹塑性过渡、加工硬化及速率效应耦合关系。针对上述问题，基于9组Q195钢室温单向拉伸实验数据（样本级平均应变速率1.00&amp;times;10⁻&amp;sup3;~1.70&amp;times;10⁻&amp;sup1; s⁻&amp;sup1;），提出融合时序卷积网络（Temporal Convolutional Network, TCN）与Transformer 编码器的序列回归模型（TCN-Transformer），用于预测不同应变速率下的完整工程应力-应变曲线。模型以工程应变、瞬时应变速率和因果平均应变速率为输入，通过TCN提取局部曲线形态，并利用Transformer Encoder建立全局加载历史依赖；采用嵌套留一交叉验证（nested leave-one-out cross-validation, nested LOOCV）进行超参数选择与泛化评估。结果表明，TCN-Transformer的MAE、RMSE和R&amp;sup2;分别为3.40 MPa、5.22 MPa 和0.9849，优于J-C模型和SVR；其极限抗拉强度（UTS）应力MAE为1.91 MPa。特征消融与Gradient SHAP分析表明，速率相关特征对峰值强度和曲线重建均具有重要贡献。研究结果可为小样本条件下低碳钢应力-应变曲线的数据驱动建模提供参考。</abstract><keywords>Q195 钢,应力- 应变曲线,TCN-Transformer,嵌套留一交叉验证,Johnson-Cook本构模型</keywords></article-meta></front><body/><back><ref-list><ref id="B1" content-type="article"><label>1</label><element-citation publication-type="journal"><p>[1]Johnson G R, Cook W H. A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures[C]//Proc. 7th Int. Symp. Ballistics. 1983: 541-547.[2] 岳峰丽, 邵扬, 陈大勇, 等. 基于不同机器学习模型的TP2铜材流动应力-应变曲线预测[J]. 锻压技术, 2026, 51(2): 1-11.[3]Desu R K, Guntuku S C, Aditya B, et al. Support vector regression based flow stress prediction in 304 steel[J]. Procedia Materials Science, 2014, 6: 368-375.[4]Song S H. Constitutive equation, neural networks and SVR for hot deformation of 316L stainless steel[J]. Materials, 2020, 13(17): 3763.[5]Bai S, Kolter J Z, Koltun V. An empirical evaluation of generic convolutional and recurrent networks for sequence modeling[EB/OL]. arXiv:1803.01271, 2018.[6]Vaswani A, Shazeer N, Parmar N, et al. Attention is all you need[C]//NeurIPS. 2017, 30: 5998-6008.[7]Cawley G C, Talbot N L C. On over-fitting in model selection and selection bias in performance evaluation[J]. JMLR, 2010, 11: 2079-2107.[8]GB/T 700&amp;mdash; 2019. 碳素结构钢[S]. 北京: 中国标准出版社, 2019.[9]GB/T 228.1 &amp;mdash; 2021. 金属材料 拉伸试验 第1 部分: 室温试验方法[S]. 北京: 中国标准出版社, 2021.[10]Lundberg S M, Lee S I. A unified approach to interpreting model predictions[C]//NeurIPS. 2017, 30: 4765-4774.</p><pub-id pub-id-type="doi"/></element-citation></ref></ref-list></back></article>
