Abstract: In this paper, the Quantum-behaved Particle Swarm Optimization（QPSO） with Tikhonov regularization is used to solve the inverse heat conduction problem of estimating the time dependent heat transfer coefficient of a flat plate. The prior information about the functional form of the unknown is unavailable. The estimation is based on transient temperature measurements taken by the sensors imbedded in the plate, which are used in the least square model, minimized by QPSO. The detail of choosing the best regularization parameter by L-curve method is presented. Numerical experiments are performed to test the proposed method. Effects of the location and number of sensors are also investigated. Comparison with conjugate gradient method is given as well.

Key words: heat transfer coefficient, Quantum-behaved Particle Swarm Optimization（QPSO）, Tikhonov regularization, conjugate gradient method, L-curve

摘要： 量子行为粒子群优化算法（QPSO）和Tikhonov正则化方法用来求解热传导反问题，近似估计平板随时间变化的热传导系数。由于热传导系数的函数形式是未知的，所以问题可以归结为函数估计问题。求解过程是基于最小二乘模型的，采用的是嵌在平板中的传感器所测量得到的温度，优化过程由QPSO算法来求解。给出了由L曲线方法选择正则参数的详细过程。提出算法的有效性经过了数值实验的验证。传感器的位置和数量对结果的影响也做了研究。给出了与共轭梯度法的比较。

关键词: 热传导系数, 量子行为粒子群优化算法, Tikhonov正则化, 共轭梯度法, L曲线