【作者】 周明华；

【导师】 汪国昭；

【作者基本信息】 浙江大学 ， 应用数学， 2005， 博士

【摘要】 本文作者利用现代优化算法和超限插值方法分别对于化学工程、生物物理、艺术曲面造型等领域的问题进行了深入研究。分别回顾了遗传算法、人工神经网络、B样条曲线插值拟合及超限插值的发展历史及其各自特点。 以贵金属为催化剂的一氧化碳催化速率是化学工程催化研究中一个重要研究方向。考虑用B样条曲线拟合一氧化碳催化速率数据使得最小二乘拟合误差最小。一般有两种考虑，一种是保持B样条基函数的节点不变，选择参数使得拟合较优。参数的选择方法包括均匀取值、累加弦长法、centripetal model、Gauss-Newton迭代法等。另一种则是先确定好参数值(一般用累加弦长法)，然后再用某一算法计算出节点，使得拟合较优。文中同时把两者统一考虑，用遗传算法同时求出参数、节点使得拟合在最小二乘误差意义下最优。与Gauss-Newton迭代法、Piegl算法相比本方法具有较好的鲁棒性(拟合曲线与初始值无关)、较高的精度及控制顶点少等优点。实验结果说明采用遗传算法应用B样条曲线拟合一氧化碳催化速率，得到的曲线逼近效果更好，一氧化碳催化速率过程的描述更为准确。 为提高提纯塔二氧化碳出口纯度，需要建立其与进料纯度、进塔温度、塔顶压力、塔顶温度、加热温度、塔釜压力、塔釜温度七个因素之间的模型。根据实际生产数据运用人工神经网络方法建立了二氧化碳出口纯度与这七个因素之间的非线性模型。用该方法建立的非线性模型能有效地描述二氧化碳纯度与各因素之间的关系，同时通过训练好的网络能找到生产二氧化碳具有较高纯度的最佳控制点，得到了令人满意的效果。与用传统方法的线性回归模型、对数回归模型建立起来的模型相比，用人工神经网络方法建立的模型具有处理非线性模型能力强，鲁棒性好，拟合精度高，计算速度快，预测、控制能力强等优点。 荧光寿命法成像技术(FLIM)是一种非常有效、功能强大且能用来分析复杂生物组织和细胞分子的成像技术。传统的荧光寿命成像的数据分析是采取按某些具有不同寿命、离散的单参量指数模型来描述荧光衰减过程。在像生物组织这样既复杂又不均匀的样品中，虽然多参量指数模型能提供比单参量指数更多还原

【Abstract】 This paper summarized our researches on problems of Chemical Engineering, biophysics and aesthetic surfaces modelling by using genetic algorithms, nueral network and transfinite interpolation. The history and respective characters of genetic algorithms, neural network, fitting and interpolation of B-spline curve and transfinite interpolation were briefly reviewed.The studies of the catalysis rate of CO oxidation using supported noble metal catalysts are very important in chemical engineering. To obtain a good approximation for least square fitting of B-spline curve to the rate data of CO oxidation, parameters and knots have to be dealt with as variables frequently. There are two kinds of considerations. The first is to choose parameters with witch the fitting are better while the knots of the B-spline bases are in a fix. The choices of parameters include uniform parameterization, cumulative chord length parameterization, centripetal model parameterization and Gauss-Newton approach. The other is to determine parameters in advance (generally cumulative chord length parameterization) and then to compute the knots of B-spline bases by some algorithms such that the fitting become more precise. In this paper both the parameters and the knots of the B-spline bases are considered simultaneously by using genetic algorithms such that the fitting B-spline curve to data attains its optimum in the total least squares sense. With this, the parameters and the knots can be appropriately determined simultaneously. The method given in this paper have advantages of robustness (the resulting curve is initial-value-free), better precision and fewer vertexes compared with Gauss-Newton approach and Piegl’s algorithm. The experiments show that genetic algorithms-based least square fitting of B-spline to the rate data of CO oxidation are better in approximation. The catalysis process can be described precisely.To improve the purity of the carbon dioxide from the purifying column, it is necessary to build a model of the purity of carbon dioxide with seven factors of feed purity, feed temperature, column top pressure, column top temperature, column reactor heating temperature, column reactor pressure and column reactor temperature.更多还原