每年出版 6 期
ISSN 打印: 2152-5080
ISSN 在线: 2152-5099
Indexed in
PROPAGATION OF HYBRID UNCERTAINTIES IN TRANSIENT HEAT CONDUCTION PROBLEMS
摘要
In this paper, the propagation of hybrid uncertainties is studied in transient heat conduction problems. Based on the layer-by-layer analysis strategy, a novel mixed method using the stochastic theory and the convex model is presented. Two types of models for the uncertainties are considered: random parameters and uncertain-but-bounded parameters. Firstly, the matrix perturbation theory is utilized to deal with random parameters, obtaining the temperature response expectation and variance. Then using the Taylor series expansion and the Lagrange multiplier method to analyze the convex model, we derive the intervals of the temperature response probabilistic characters. Four numerical examples are presented to address transient heat conduction problems with random and uncertain-but-bounded parameters or pure uncertainties. The results are compared with those of the Monte Carlo method to verify the feasibility and practicality of the proposed method. In addition, the proposed method is also applicable to the steady-state problems.
-
Wang, C. and Qiu, Z.P., Hybrid Uncertain Analysis for Steady-State Heat Conduction with Random and Interval Parameters, Int. J. Heat Mass Transf, 80:319-328,2015.
-
Woodfield, P.L. and Monde, M., Estimation of Uncertainty in an Analytical Inverse Heat Conduction Solution, Exp. Heat Transf, 22:129-143,2009.
-
Boulorea, A., Struzika, C., and Gaudierb, F., Uncertainty and Sensitivity Analysis of the Nuclear Fuel Thermal Behavior, Nucl. Eng. Des., 253:200-210, 2012.
-
Xia, B. and Yu, D., Response Analysis of Acoustics Field with Convex Parameters, J. Vib. Acoust., 136:1-12, 2014.
-
Elishakoff, I., Three Versions of the Finite Element Method based on Concepts of Either Stochasticity, Fuzziness, or Anti-Optimization, Appl. Mech. Rev., 51:209-218, 1998.
-
Guo, Z.P., Deng, Z.M., Li, X.X., and Han, Y.W., Hybrid Uncertainty Analysis for a Static Response Problem of Structures with Random and Convex Parameters, Acta Mech, 228:2987-3001,2017.
-
Shah, H., Hosder, S., and Winter, T., A Mixed Uncertainty Quantification Approach Using Evidence Theory and Stochastic Expansions, Int. J. Uncertain. Quantif., 5(1):21-48, 2015.
-
Nicola, B.M., Egea, J.A., Scheerlinck, N., Bang, J.R., and Datta, A.K., Fuzzy Finite Element Analysis of Heat Conduction Problems with Uncertain Parameters, J. Food Eng., 103:38-46, 2011.
-
Eisentraudt, M. and Leyendecker, S., Fuzzy Uncertainty in Forward Dynamics Simulation, Mech. Sys. Signal Process, 126:590-608,2019.
-
Impollonia, N. and Muscolino, G., Interval Analysis of Structures with Uncertain-But-Bounded Axial Stiffness, Comput. Methods Appl. Mech. Eng., 200:1945-1962,2011.
-
Deng, Z.M., Guo, Z.P., and Zhang, X.D., Non-Probabilistic Set-Theoretic Models for Transient Heat Conduction of Thermal Protection Systems with Uncertain Parameters, Appl. Therm. Eng., 95:10-17, 2016.
-
Shome, B., Monte Carlo based Uncertainty Analysis for Variable Property Mixed Convection Flow in a Uniformly Heated Circular Tube, Int. J. Uncertainty Quantif., 6:417-428, 2016.
-
Hua, Y.C., Zhao, T., and Guo, Z.Y., Transient Thermal Conduction Optimization for Solid Sensible Heat Thermal Energy Storage Modules by the Monte Carlo Method, Energy, 133:338-347,2017.
-
Hua, X.G., Ni, Y.Q., Chen, Z.Q., and Ko, J.M., An Improved Perturbation Method for Stochastic Finite Element Model Updating, Int. J. Numer. Methods Eng., 73:1845-1864, 2008.
-
Chiba, R., Stochastic Thermal Stresses in an Annular Disc with Spatially Random Heat Transfer Coefficients on Upper and Lower Surfaces, Acta Mech., 194:67-82, 2007.
-
Hien, T.D. and Kleiber, M., Stochastic Finite Element Modelling in Linear Transient Heat Transfer, Comput. Methods Appl. Mech. Eng., 144:111-124, 1997.
-
Zhao, L. and Chen, Q., Neumann Dynamic Stochastic Finite Element Method of Vibration for Structures with Stochastic Parameters to Random Excitation, Comput. Struct., 77:651-657,2000.
-
Xiu, D.B. and Karniadakis, G.E., A New Stochastic Approach to Transient Heat Conduction Modeling with Uncertainty, Int. J Heat Mass Transf., 46:4681-4693,2003.
-
Yang, T.J. and Cui, X.Y., A Random Field Model based on Nodal Integration Domain for Stochastic Analysis of Heat Transfer Problems, Int. J Therm. Sci., 122:231-247,2017.
-
Blatman, G. and Sudre, B., An Adaptive Algorithm to Build Up Sparse Polynomial Chaos Expansions for Stochastic Finite Element Analysis, Prob. Eng. Mech, 25:183-197, 2010.
-
Moens, D. and Vandepitte, D., Recent Advances in Non-Probabilistic Approaches for Non-Deterministic Dynamic Finite Element Analysis, Arch. Comput. Methods Eng., 13:389-464, 2016.
-
Wang, Z., Tian, Q., and Hu, H., Dynamics of Flexible Multibody Systems with Hybrid Uncertain Parameters, Mech. Mach. Theory, 121:128-147,2018.
-
Yin, S.W., Yu, D.J., Luo, Z., and Xia, B.Z., Unified Polynomial Expansion for Interval and Random Response Analysis of Uncertain Structure-Acoustic System with Arbitrary Probability Distribution, Comput. Methods Appl. Mech. Eng., 336:260.
-
Sofi, A. and Romeo, E., A Unified Response Surface Framework for the Interval and Stochastic Finite Element Analysis of Structures with Uncertain Parameters, Probab. Eng. Mech, 54:25-36,2018.
-
Wang, C., Qiu, Z.P., and He, Y.Y., Fuzzy Stochastic Finite Element Method for the Hybrid Uncertain Temperature Field Prediction, Int. J. Heat Mass Transf., 91:512-519,2015.
-
Chong, W., Zhiping, Q., Menghui, X., and Yunlong, L., Novel Reliability-Based Optimization Method for Thermal Structure with Hybrid Random, Interval and Fuzzy Parameters, Appl. Math. Model, 47:573-586, 2017.
-
Wang, C., Matthies, H.G., Xu, M., and Li, Y., Dual Interval-and-Fuzzy Analysis Method for Temperature Prediction with Hybrid Epistemic Uncertainties via Polynomial Chaos Expansion, Methods Appl. Mech. Eng., 336:171-186,2018.
-
Fu, C.M., Cao, L.X., Tang, J.C., and Long, X.Y., A Subinterval Decomposition Analysis Method for Uncertain Structures with Large Uncertainty Parameters, Comput. Struct., 197:58-69, 2018.
-
Ben-Haim, Y. and Elishakoff, I., Convex Models of Uncertainty in Applied Mechanics, Amsterdam: North Holland, pp. 63-187, 1990.
-
Stewart, G.W. and Sun, J., Matrix Perturbation Theory, New York: Academic Press, pp. 114-265, 1990.
-
Wu, D., Gao, W., Song, C., and Tangaramvong, S., Probabilistic Interval Stability Assessment for Structures with Mixed Uncertainty, Struct. Saf., 58:105-118, 2016.
-
Li, J.P., Chen, J.J., and Zhou, C.J., Perturbed Numerical Algorithm of Non-Probabilistic Convex Set Theoretical Models for Temperature Field, J. Southwest Jiaotong Univ., 44:1-5, 2009.
-
Wang, C., Qiu, Z.P., and Wu, D., Numerical Analysis of Uncertain Temperature Field by Stochastic Finite Difference Method, Sci. China Phys. Mech, 57: 698-707,2014.