Improved numerical prediction and reliability-based optimization of transient heat conduction problem with interval parameters

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• 作者：Chong Wang (1)
  Zhiping Qiu (1)
  
  1. Institute of Solid Mechanics ; Beihang University ; Beijing ; 100191 ; People鈥檚 Republic of China
  
• 关键词：Temperature field prediction ; Interval uncertainties ; High ; order Neumann expansion ; Parameter perturbation method ; Reliability ; based optimization
• 刊名：Structural and Multidisciplinary Optimization
• 出版年：2015
• 出版时间：January 2015
• 年：2015
• 卷：51
• 期：1
• 页码：113-123
• 全文大小：1,068 KB
• 参考文献：1. Bapanapalli SK, Martinez OA et al (2006) Analysis and design of corrugated-core sandwich panels for thermal protection systems of space vehicles. In: 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Material Conference. Newport, Rhode Island, Paper No. 2006鈥?876
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• 刊物类别：Engineering
• 刊物主题：Theoretical and Applied Mechanics
  Computer-Aided Engineering and Design
  Numerical and Computational Methods in Engineering
  Engineering Design
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1615-1488

文摘

In this paper, a high-order interval parameter perturbation method (HIPPM) and a reliability-based optimization model are proposed to solve the transient heat conduction problem with uncertainties in both the material properties and initial/boundary conditions. Interval variables are used to quantitatively describe the uncertain parameters with limited information. A modified stability theory is proposed and used to select space step and time step in the interval discrete schemes. Compared with the traditional first-order perturbation method, HIPPM can yield more accurate ranges of the uncertain temperature field by adopting the higher order terms of the Neumann series to approximate the interval matrix inverse. In the following investigated optimization model, a satisfaction degree of interval is employed to deal with the interval constraint functions. Given a reliability index representing the confidence level, uncertain constraints can be transformed into deterministic ones. The proposed HIPPM is used to predict the intervals of the constraints, and whereby eliminate the optimization nesting. A numerical example modeling a thermal protection system is presented to demonstrate the feasibility and efficiency of the proposed method.