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Mathematical Modeling and Inverse Problem Approaches for Functional Clothing Design Based on Thermal Mechanism

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Proceedings of the Forum "Math-for-Industry" 2018

Part of the book series: Mathematics for Industry ((MFI,volume 35))

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Abstract

Functional clothing design is of paramount importance in the clothing industry, and the thermal comfort clothing (TCC) and thermal protective clothing (TPC) are the two kinds of functional clothing satisfying the thermal comfort and thermal safety, respectively. It is therefore important to reveal heat and moisture transfer characteristics in the system of human body–clothing–environment, which directly determine thermal comfort level or thermal safety level of human body. Based on the thermal mechanism such as heat/moisture transfer in porous fabric, we present some parabolic equation models or space-fractional models, respectively. Hence, we formulate inverse problems of textile material determination (in abbreviation, IPTMD) for the TCC/TPC design. Adopting the idea of least squares method or regularization method and Bayesian statistical inference method, we formulate the IPTMD into a function minimization problem. Combined with the numerical methods for PDEs, some numerical algorithms of approximated solutions for the IPTMD are reviewed in the sense of the deterministic and stochastic structure, respectively. Theoretical study and numerical simulation results validate the formulation of the IPTMD and demonstrate the effectiveness of the proposed numerical algorithms.

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Acknowledgements

This research is supported by the National Natural Science Foundation of China (No. 11871435 and 11471287). The work was elected as a plenary talk on the Forum “Math-for-Industry” 2018– Big Data Analysis, AI, Fintech, Math in Finances and Economics, November 17–21, 2018, Shanghai, China.

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Authors and Affiliations

  1. Department of Mathematics, College of Sciences, Zhejiang Sci-Tech University, Hangzhou, 310018, Zhejiang Province, People’s Republic of China

    Dinghua Xu

  2. School of Mathematics, Shanghai University of Finance and Economics, Shanghai, 200433, People’s Republic of China

    Dinghua Xu & Tingyue Li

Authors
  1. Dinghua Xu
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  2. Tingyue Li
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Correspondence to Dinghua Xu .

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Editors and Affiliations

  1. School of Mathematical Sciences, Fudan University, Shanghai, China

    Jin Cheng

  2. Shanghai University of Finance and Economics, Shanghai, China

    Xu Dinghua

  3. Institute of Mathematics for Industry, Kyushu University, Fukuoka, Japan

    Osamu Saeki

  4. Institute of Mathematics for Industry, Kyushu University, Fukuoka, Japan

    Tomoyuki Shirai

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Xu, D., Li, T. (2021). Mathematical Modeling and Inverse Problem Approaches for Functional Clothing Design Based on Thermal Mechanism. In: Cheng, J., Dinghua, X., Saeki, O., Shirai, T. (eds) Proceedings of the Forum "Math-for-Industry" 2018. Mathematics for Industry, vol 35. Springer, Singapore. https://doi.org/10.1007/978-981-16-5576-0_4

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