Research On Boundary Condition Inverse Problem In Heat Conduction Based On Improved Firefly Algorithm

Inverse heat conduction problems(IHCPs)in estimating boundary conditions have extensive application in aerospace and industrial manufacture field.How to identify the boundary temperature and heat flux has become an important research topic in IHCPs field.Computational method is studied to identify boundary conditions of two-dimensional steady state and transient IHCPs.Conventional boundary element method(BEM)and dual reciprocity BEM are used for solving the direct heat conduction problem(DHCP),respectively.For the steady state IHCPs,the unknown boundary condition is approximated by polynomial function.Thus,the inverse problem in identifying the boundary condition is transformed into estimating the coefficients of polynomial function.The method mentioned above reduces the number of undetermined parameters apparently.The improved firefly algorithm is applied to solve the inverse problem.Estimation of boundary conditions for isotropic and orthotropic material is investigated,respectively.The influence of the measurement point number and measurement noise is discussed in these two IHCPs,in addition,the effect of discrete boundary element number is also considered in analyzing orthotropic material IHCPs.Numerical examples indicate that,for both isotropic and orthotropic material,when the measurement point number is not enough,the estimated results are bad.With the increase of measurement point number,the results become more accurate.Measurement noise also has great influence on identifying boundary conditions,with the decrease of measurement noise,results are more accurate.The discrete boundary element number has great influence on estimating boundary conditions of orthotropic material,with the increase of discrete boundary element number,the estimated boundary conditions are more accurate.For transient IHCPs with heat source,dual reciprocity method is applied to transform domain integrals caused by heat source function and temporal derivative into boundary integrals.The firefly algorithm owns excellent global search ability.However,the speed of firefly algorithm is slow because of its randomness.The Newton method is introduced in order to increase convergent speed.The improved firefly algorithm not only has strong global search ability but also has good local search ability.The measurement number and measurement noise are considered in identifying transient boundary conditions.Results show that it is hard to obtain accurate estimated boundary conditions when measurement points are insufficient.With the increase of measurement point number,the estimated boundary conditions are more accurate.Results indicate that with the decrease of measurement noise,estimated boundary condition are more accurate when consider the influence of measurement noise in transient IHCPs.Numerical results also indicate that the more front the time substep is,the more accurate the estimated boundary conditions are.