【作者】 朱星键；

【导师】 蔡从中；

【作者基本信息】 重庆大学 ， 凝聚态物理， 2011， 硕士

【摘要】 回归分析是数理统计学中应用最广泛的一个分支,传统的回归学习算法都以经典统计数学的渐近理论为依据,统计规律只有在已知样本数无限多时才显露出来。针对经典统计数学这一弱点,Vapnik学派在1995年提出了“统计学习理论”和“支持向量机（Support Vector Machine, SVM）”。支持向量机在少量样本时也可用于分类和回归研究,并且具有很好的泛化能力,已被广泛应用于多个领域的实际问题研究中。粒子群优化算法（Particle Swarm Optimization, PSO）是一种基于群体智能理论的新兴演化计算技术。Sun等人从量子力学的角度,通过对粒子收敛行为的研究,基于PSO算法提出了量子粒子群算法（Quantum-behaved Particle Swarm Optimization, QPSO）。由于具有量子行为的粒子满足聚集态的性质完全不同,使粒子能在整个可行的解空间中进行搜索寻求最优解,因而QPSO算法在搜索能力上远远优于所有已开发的PSO算法。本论文采用了多种传统和现代的数据回归理论与方法,针对功能薄膜等材料的实验数据进行回归计算研究。重点是结合QPSO优化算法和支持向量回归（Support Vector Regression, SVR）方法对全介质光学膜、质子交换膜燃料电池、Bi系超导材料和Co₃O₄纳米粒子等功能材料的性能参数及实验结果进行回归预测,并比较这些算法的性能和误差。同时还在已建立的SVR模型基础了进行了因素分析、工艺参数优化和灵敏度分析等。本文研究的主要内容有:①简要说明了功能薄膜材料的研究现状和实际问题。介绍了几种常用的传统和现代回归方法及其原理,包括多元线性回归、偏最小二乘回归、概率神经网络和极限学习机,分析了它们的优缺点。然后阐述了统计学习理论的基本思想,并对支持向量回归原理进行了详细的叙述。②介绍了PSO算法的基本原理及其改进与发展,简述了QPSO算法的基本原理。此外,还简要给出了多种常用的参数优化算法的原理,如遗传算法、差分进化算法、分散搜索算法、网格搜索算法、模拟退火算法和蚁群算法等。③根据全介质光学膜、质子交换膜燃料电池、Bi系超导材料和Co₃O₄纳米粒子等多组实验数据,应用QPSO-SVR等多种回归方法对它们进行建模和预测,并对比了模型的预测结果和泛化性能。④在已建立的QPSO-SVR模型的基础上,对质子交换膜燃料电池、Bi系超导材料和Co₃O₄纳米粒子等实验进行了因素分析,提出了优化的工艺参数。由研究结果可以看出,基于QPSO优化的SVR模型的预测精度优于多元线性回归、神经网络等回归方法,且泛化能力也比其它方法要强。这表明SVR是一种行之有效的数据处理分析方法,有望在研究和开发新型功能薄膜材料等方面发挥其重要的作用。更多还原

【Abstract】 Regression analysis is one of the most widely used branch in the mathematical statistics. The traditional regression algorithms are all based on the asymptotic theory of classical statistical mathematics, where the statistical rule is exposed only when the number of samples approximating infinite. For that weakness, Vapnik and co-workers proposed the statistical learning theory （SLT） and support vector machine （SVM） in 1995. Even in the case of small-sample database, SVM could still be adopted in classification and regression analysis with preferable generalizing performance, so that it has been extensively applied to tackle many real-world problems in various fields. Particle swarm optimization （PSO） is a novel evolutionary computing approach based on swarm intelligence theory. From the view of quantum mechanics, Sun et al. proposed the quantum-behaved particle swarm optimization （QPSO） via the research on particle convergence behaviour. Because the quantum-behaved particles meet completely different aggregation property, the optimal solution could be searched out in the whole solution space, so that QPSO algorithm is superior to all the kinds of previous proposed PSO algorithms.In this thesis, many traditional and modern regression approaches are employed for regression analysis based on the experimental datasets of functional thin film materials. It is focused on the application of SVR method combined with QPSO for physical properties prediction on some functional materials including nitrogen-oxygen compound dielectric thin film, proton exchange membrane fuel cell, Bi-system superconductivity material and Co₃O₄ nanoparticles. Meanwhile, the multifactor analysis, process parameter optimization and sensitivity analysis is carried out based on the established QPSO-SVR models.The main contents of this thesis are as follows:1. The current status and problems on the functional thin film material research were generally introduced. The regression principles of popular regression methods such as multivariable linear regression （MLR）, partial least square regression （PLS）, probabilistic neural network （PNN） and extreme learning machine （ELM）, were reviewed briefly. The principle of SLT and SVR algorithm were described in detail.2. The principle, algorithm and development of PSO were introduced, especially for QPSO method. Moreover, some optimization methods, including genetic algorithm （GA）, differential evolution （DE）, scatter search （SS）, grid search algorithm （GSA）, simulated annealing （SA） and ant conoly optimization （ACO） were reviewed. The advantages and disadvantages of these algorithms were also summarized.3. Based on the experimental datasets of nitrogen-oxygen compound dielectric thin film, proton exchange membrane fuel cell, Bi-system superconductivity material and Co₃O₄ nanoparticles, QPSO-SVR and other regression approaches were employed to model and predict the physical properties, as well as their predicted results and generalizing performance were compared.4. Based on the established QPSO-SVR models, the multi-factor analyses on the proton exchange membrane fuel cell, Bi-system superconductivity material and Co₃O₄ nanoparticles were conducted and the optimal process conditions were proposed.The studies of above demonstrated that the prediction precison of QPSO-SVR was superior to those of other regression methods including multivarivate linear regression, neural network and so on, and its generalization ability surpasses those of them. The results suggest that SVR is an effective and powerful technique, and it may be further developed to be a potential application tool in research and development of novel functional thin film materials.更多还原