Maximum Likelihood Estimation of Radial Basis Function Neural Networks for Process Control

过程控制径向基函数神经网络的最大似然估计

• 批准号: 9504407
• 负责人: Lyle Ungar
• 金额: $ 12万
• 依托单位: University of Pennsylvania
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-06-15 至 1999-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9504407&HistoricalAwards=false
• 关键词: Maximum; Likelihood; Estimation; Radial; Basis

Abstract - Ungar Radial Basis Functions (RBFs) are a class of artificial neural networks for process control applications. Commonly, the k-Means clustering algorithm is applied to the predictor ( independent variables), after which a linear regression layer maps the hidden unit activations to the appropriate responses (dependent variables). The PIs plan to explore an RBF architecture which is suited to statistical analysis. The statistical model underlying the architecture is a mixture model in which the mixture coefficients are radial basis functions and the mixture components are constant or polynomial functions. Depending on the assumptions used to generate the model, different generalizations of radial and elliptical basis functions result. This allows the use of the expectation maximization (EM) technique for finding maximum likelihood estimators of the parameters. In addition, algorithms will be developed to partially invert the networks, estimate the local prediction error of the network, recognize novel data points, automatically select the number of basis functions, and incrementally update the network efficiently as data are collected. The techniques will be tested on real data from chemical plants, compared to other approximation methods with respect to speed and accuracy, and modified as needed to achieve fast, accurate, and robust performance. This is a coordinated project between two investigators, a mathematician and a chemical engineer, at two different institutions. Industrial data are to be provided by the DuPont Company.

摘要- Ungar径向基函数（RBFs）是一类用于过程控制应用的人工神经网络。 通常，k-Means聚类算法应用于预测变量（自变量），之后线性回归层将隐藏单元激活映射到适当的响应（因变量）。 PI计划探索适合统计分析的RBF架构。 该体系结构的统计模型是一个混合模型，其中混合系数是径向基函数，混合分量是常数或多项式函数。 根据用于生成模型的假设，会产生径向基函数和椭圆基函数的不同概括。 这允许使用的期望最大化（EM）技术，寻找最大似然估计的参数。 此外，还将开发算法来部分反转网络，估计网络的局部预测误差，识别新的数据点，自动选择基函数的数量，并在收集数据时有效地增量更新网络。 这些技术将在来自化工厂的真实的数据上进行测试，与其他近似方法在速度和准确性方面进行比较，并根据需要进行修改，以实现快速，准确和强大的性能。 这是两个研究人员之间的协调项目，一个数学家和一个化学工程师，在两个不同的机构。 工业数据由杜邦公司提供。