Abstract:

With thermo-gram, parameters of tumor inside can be estimated, and an inverse heat conduction model with unknown inner heat source could be obtained from it, and the solving process need a large number solutions of the heat conduction problem, where temperature field in the sub-domain is calculated. For 3D model, it needs a relatively long time. Particle swarm optimization combined with least square methods was applied to solve the inverse problem, in which least square method was used to predict particle's value of fitness function. During the solution process, some of the particles are going to be excluded from the group, by the judgment of new definition of distance. Hence, these particles' positions were rearranged. This method consumes less time than the modified PSO mentioned above, without sacrificing accuracy. Prediction coefficient was analyzed to find how it influences the searching process. So linear decreasing prediction coefficient was applied. Numerical verification shows that above method can reduce the numbers of solution of heat conduction, shorten the solving time, without sacrificing accuracy.

Key words: inverse heat conduction problem, least square method, prediction, algorithm, imaging

摘要：

根据体表红外热像图获得体内异常热源信息可抽象为一个含有未知内热源的导热反问题，其求解过程需要对计算区域内温度场进行反复计算，对于复杂的三维物理模型反演过程耗时较长。采用粒子群算法用以反演未知参数，并结合最小二乘法对部分粒子位置对应的目标函数值进行预测。在反演过程中，对远离群体的粒子进行位置的重新分配，避免计算资源的浪费。分析不同预测系数对粒子搜索过程的影响，采用了线性递减的预测系数。数值验证结果表明：基于最小二乘法预测的粒子群算法能在保证反演精度的前提下减少导热问题计算次数，缩短反演所需时间。

关键词: 导热反问题, 最小二乘法, 预测, 算法, 成像