基于GP模型的非线性系统建模及其应用

发布时间：2018-03-07 10:07

  本文选题：数据驱动建模　切入点：高斯过程模型　出处：《浙江大学》2016年博士论文　论文类型：学位论文

【摘要】：随着当今工业信息化、数字化进程的不断深入,数据驱动建模(data-driven modeling)方法及其应用引起了广泛关注。高斯过程(Gaussian process, GP)模型通过对训练数据相关性的分析,可以显式地给出预测值的后验概率分布,从而反映了预测值的不确定性。这一特性使得它在处理模型不精确时的预测、控制、优化等问题时具有很大优势。此外,GP模型本身还具有易于实现、超参数自适应获取等优势,逐渐成为了机器学习领域的研究热点之一,并在过程系统工程领域得到了广泛应用。本文围绕GP模型在不同类型工业过程中的建模及相关应用开展研究并取得以下成果：1.利用GP模型所提供的预测方差信息,提出了自主动的GP模型,建立了更新数据的自主筛选策略,使用预测方差和预测误差相结合的方式对模型预测值不准确的情况作出区分,以更好的选择建模数据。2.基于GP模型所提供的预测分布,提出了一种被称为“基于自主改进GP模型的预测控制(AI-GPMPC)"方法,适用于初始模型不准确情况下的设定值快速追踪控制问题。该方法能够在“搜索当前模型所提供的信息”和“探索可能改善控制效果的未知区域”之间进行权衡,在对系统输出进行有效控制的同时,通过更新训练集改进预测模型。3.提出了KL-GP的分布参数系统建模方法,借助KL分解对过程进行时空分解和维度缩减,并在各空间维度中分别建立GP模型后,通过时空合成对原过程进行重构获得输出预测。考虑模型更新的需要,对KL-GP方法进行扩展,提出了“自主动KL-GP (SA-KL-GP)"的建模方法,利用所得的输出预测方差对任意时空点上的建模效果进行评价,并自主选取数据以改进当前模型。为满足实时模型改进的要求,提出了改进的“迭代选择KL-GP (RS-KL-GP)"建模方法,利用迭代更新方法减少了更新计算量。4.针对间歇过程训练数据稀缺导致模型不准确的问题,提出了一种基于GP模型和期望改进进行批次间最优轨迹的设计方法。以不准确预测模型为前提,利用“期望改进量”的作为优化目标,该方法可以通过尽量少的试验性生产批次得到最优的过程产品质量。5.基于过程机理知识,建立了低压化学气相沉积(LPCVD)过程的仿真研究对象；使用GP模型建立预测模型,利用有限的训练数据对含有空间分布信息的批次过程进行建模,用以预测空间分布的晶圆表面薄膜厚度。在进行优化控制的过程中,基于GP模型所提供的预测值不确定性,优化选择下一批次的操作变量,以保证过程的稳定性。此外,预测不确定性也被用于更新GP模型的高效数据选择,尽量减少数据采样,同时增强模型质量。
[Abstract]:With the development of industry information and digitization, data-driven modeling method and its application have attracted much attention. Gao Si process Gaussian process (GP) model is analyzed by analyzing the correlation of training data. The posteriori probability distribution of the prediction value can be given explicitly, which reflects the uncertainty of the prediction value. In addition, the GP model itself has the advantages of easy implementation and super parameter adaptive acquisition, which has gradually become one of the research hotspots in the field of machine learning. And has been widely used in the field of process systems engineering. This paper focuses on the modeling and related applications of GP model in different types of industrial processes, and obtains the following results: 1. Using the prediction variance information provided by GP model, A self-active GP model is proposed, and an independent screening strategy for updating data is established. The inaccurate prediction value is distinguished by combining the prediction variance with the prediction error. Based on the prediction distribution provided by GP model, a method called "predictive control based on autonomous improved GP model (AI-GPMPC)" is proposed. This method is suitable for fast tracking control problems where the initial model is inaccurate. This method can be balanced between "searching for information provided by the current model" and "exploring unknown areas that may improve the control effect". While the system output is effectively controlled, the prediction model is improved by updating the training set. (3) the distributed parameter system modeling method of KL-GP is proposed. The process is decomposed and dimensionally reduced by KL decomposition. After the GP model is established in each dimension, the output prediction is obtained through the reconstruction of the original process by space-time synthesis. Considering the need of model updating, the KL-GP method is extended, and the modeling method of "self-active KL-GP SA-KL-GP" is proposed. In order to meet the requirements of real-time model improvement, an improved "iterative selection KL-GP RS-KL-GP" modeling method is proposed to evaluate the modeling effect at any time and space points by using the output predictive variance obtained, and to select the data independently to improve the current model, in order to meet the requirements of real-time model improvement, an improved" iterative selection KL-GP RS-KL-GP" modeling method is proposed. The iterative updating method is used to reduce the updating computation. 4. Aiming at the problem of model inaccuracy caused by the scarcity of training data in batch process, A design method of optimal trajectory between batches based on GP model and expectation improvement is proposed. Based on the inaccurate prediction model, the "expected improvement quantity" is used as the optimization objective. Based on the knowledge of process mechanism, the simulation object of low pressure chemical vapor deposition (LPCVD) process is established, and the prediction model is established by using GP model. The batch process containing spatial distribution information is modeled with limited training data to predict the thickness of the spatially distributed wafer surface film. In the process of optimization control, the prediction value is uncertain based on GP model. The operation variables of the next batch are optimized to ensure the stability of the process. In addition, the prediction uncertainty is also used to update the efficient data selection of GP model to minimize data sampling and enhance the quality of the model.
【学位授予单位】：浙江大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O211.6
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本文编号：1578988