The Trajectory Optimization For Batch Processes Based On Similarity Of Principal Components

With the increasing demand of multi-specifications,multi-varieties and high quality products in modern society,batch processes characterized by small quantity and high added value develop rapidly.From the point of view of process control,the batch processes can be divided into five levels: planning decision,production scheduling,manipulated trajectory optimization,process control and sequential control.The manipulated trajectory optimization is at the core of process control.Specifically,it is the goal of control layer and the basis of scheduling layer,so it has become the focus in both industry and academia.Batch processes have no stable working points with complex dynamic and nonlinear properties and the production demand changes with the market,so it is difficult to research on optimization based on mechanism model.On the other hand,the repetitive running characteristics of batch processes make the process data valuable for manipulated trajectory optimization.Favorable information mined from the data of past batches can be used to guide the production of subsequent batches.Therefore aiming at manipulated trajectory optimization problems of batch processes,a new data-driven optimization strategy is proposed.Considering the redundancy of data information and the multi-stage feature of the process,the strategy has been improved furtherly.The details are as follows:(1)The manipulated trajectory optimization strategy based on similarity of principal components is proposed.Firstly the time-segmental variables and the controlled quality index variable are acquired with piecewise discretization.Then the high dimensional matrix is then transformed into the lower dimensional one by using PCA(Principal Component Analysis)algorithm and the manipulated trajectory is optimized based on the cosine similarity between time-segmental variables and the controlled quality index variable in the lower dimensional plane.Finally,in order to deal with the real-time applications,the recursive algorithm is obtained to update the manipulated trajectory.(2)To make full use of information in time-segmental variables,and to enhance the explanatory effect of time-segmental variables on the controlled quality index variable,the above optimization scheme is improved with OSC(orthogonal signal correction)algorithm.Firstly the index-relevant subspace is defined and the basis of background space is calculated.The index-relevant information is extracted from time-segmental variables after correction.Then the dimension of the corrected variables is reduced with principal component analysis algorithm and the manipulated trajectory is optimized by cosine similarity between the time-segmental variables and the controlled quality index variable in the low dimensional plane.Finally,the index-relevant information of new batches is extracted to update the standard deviation and cosine similarity.(3)Taking the multistage characteristics of batch processes into account,the above optimization scheme is improved continuously by the idea of piecewise optimization and fusion.Firstly timeslice matrices are divided and time-slice loading matrices are acquired by principal component analysis algorithm.The clustering algorithm is applied to weighted time-slice loading matrices to get the stages of the processes.Then at each stage,the stage index-relevant information is extracted from time-segmental variables by orthogonal signal correction algorithm.The manipulated trajectories are corrected based on the cosine similarity between time-segmental variables and the controlled quality index variable.Next the weight coefficient is acquired by calculating correlation coefficient between each stage and the controlled quality index variable and the stage manipulated trajectories are fused with the weight coefficient.Finally,when the recursive algorithm is applied,stage trajectories are updated respectively and fused with the calculated weight coefficient.The crystallization process of Bisphenol A is a type of complex multi-stage batch process.It is difficult to obtain the mechanism model and the characteristics of process data are complicated.All the schemes have been employed in the temperature trajectory optimization of Bisphenol A crystallization process and the results have illustrated the effectiveness and benefit.