Nonlinear Systems Modeling And Application Based On GP Models

Nowadays, with the development of informatization and digitization in the industries, researchers and engineers all over the world have been paying more and more attention to data-driven modeling and its application. By analyzing the relationship among given training data, Gaussian process (GP) model can provide an explicit posterior distribution of the predictions, which can be utilized as a fair criterion of uncertainties of these predictions. This property makes it have absolute advantages for predicting, controlling, optimizing based on some uncertain or unfaithful initial model. Besides, GP model is also of easy implementation, self-adjusting hyper-parameters. All of these advantages lead GP model as the immediate areas of research and practical applications focus, in both machine learning and process system engineering. This thesis is focus on the modeling using GP model and its applications for various processes with different characteristics, which is premised on the lack of initial training data. And the following issues are addressed in this work:1. By utilizing the uncertainties of predictions that provided by GP models, the self-updating GP model is proposed. In addition, rely on the difference between the predictive variance and traditional predictive error, a data selecting strategy is also proposed to distinguish various reasons leading to inaccurate predictions. Thus, this distinction can be utilized to handle different data using different methods when modeling the system.2. Based on the predictive distribution, an active-improving GP model based predictive control, i.e. AI-GPMPC, is proposed. This nonlinear predictive control algorithm is designed especially for the controlling tasks based on initial inaccurate model, which is caused by lack of training data. This controlling algorithm can explore the uncertain parts of model as well as exploit the information of current model. With adaptive updating of the training set efficiently, the control performance is able to be improved as well.3. A KL-GP modeling method is addressed for distributed parameter systems based on KL decomposition and GP model. The KL decomposition is employed to accomplish spatiotemporal dissolution and obtain the spatial basis functions. GP models are applied to establish the relationship of projected temporal variables. The predictions on any spatial-temporal point can be obtained by spatiotemporal synthesis. SA-KL-GP is proposed by extending KL-GP method to update the model. The predictions are evaluated to decide whether the corresponding samples are necessary for modeling. Only these so called active data with useful information are added into the training set. Besides, to satisfy the requirement of online model updating, an iterative algorithm called RS-KL-GP is also proposed to reduce computational load.4. For the batch process, who’s training data is sometimes scarce or hard to sample, the model will also be with poor-performance. To optimize the trajectory of manipulated variables batch-to-batch, an optimization method based on expected improvement and GP model is proposed. Even based on inaccurate initial model, the method can design an optimal trajectory which leads to best production quality through as few experimental producing batches as possible.5. Based on the process knowledge, a first-principle model is firstly established as platform for a LPCVD process. This batch process is also of spatial distributed characteristic. GP model is employed as predictive model to predict the thicknesses of thin film on the wafers. The manipulated variables must be designed cautiously, because a poor batch will cause heavy loss. Therefore, the predictive variances, as well as predictions, from GP model are take into account when design the MVs for next batch. Considering that the samples from the practical process are obtained by destructive measuring, the variances are also utilized as the creation of selecting data for updating model to decrease the number of samples.