This article introduces a step-by-step optimization method based on the radial basis function (RBF) surrogate model and proposes an improved expected improvement selection criterion to better the global performance of this optimization method. Then it is applied to the optimization of packing profile of injection molding process for obtaining best shrinkage evenness of molded part. The idea is first, to establish an approximation function relationship between shrinkage evenness and process parameters by a small size of design of experiment with RBF surrogate model to alleviate the expensive computational expense in the optimization iterations. And then, an improved criterion is used to provide direction in which additional training samples could be added to better the surrogate model. Two test functions are investigated and the results show that stronger global exploration performance and more precise optimal solution could be obtained with the improved method at the expense of increasing the infill data properly. Furthermore the optimal solution of packing profile is obtained for the first time which indicates that the type of optimal packing profile should be first constant and then ramp-down. Subsequently, the discussion of this result is given to explain why the optimal profile is like that.

In the present work, a multiphase calibration modeling and statistical analysis strategy is developed for the improvement of process understanding and quality prediction. Having realized the phase-wise local and cumulative effects on quality interpretation and prediction, the major task lies in how to qualify and quantify them among multiple phases. The proposed scheme is presented on two different levels: On the first level, phase-specific variable selection and O2-PLS are designed focusing on revealing the local effects of individual phases on quality variations, e.g. within the current phase, which part of process variations are responsible for quality variations and which quality variations are dominated. Moreover, bootstrapping technique is employed during the procedure of variable selection and O2-PLS, which can enhance the reliability and robustness of calibration analysis. On the second level, conventional PLS is used to model the quantitative relationship between multiple phases and the final qualities so that the cumulative effects on quality variations are apprehended by additively stacking the local contributions of various phases. The proposed strategy highlights such an idea that in real multiphase processes, each phase may only explain one part of quality variations and the final qualities can only be additively and jointly defined by multiple phases. A benchmark simulation of fed-batch penicillin fermentation production is considered and put into illustration, which demonstrates the efficiency of the proposed algorithm for better process understanding and quality interpretation in multiphase processes.

Under the influence of various exterior factors, batch processes commonly involve normal slow variations over batches, in which the changing underlying behaviors make their modeling and monitoring a greater challenge. Having realized the problems associated with the commonly adopted adaptive methods, in the present work, our biggest concern is how to minimize the efforts for long-term model updating adjustment and simultaneously maintain their validity as permanently as possible once the initial models are built. It is implemented from the viewpoint of between-batch relative changes, which are regular with process evolution and conform to certain evolving rule and statistical characteristics. First, difference subspace is constructed by calculating the between-batch difference trajectories, which represent the batchwise relative changes resulting from the slow-varying behaviors. Then their variability along batch direction is addressed and analyzed in the difference subspace using ICA-PCA two-step feature extraction, which reveals the evolving rule and statistical characteristics of slow variations. In this way, the mode of normal slow changes is extracted, trained, and modeled, which, thus, endows the initial monitoring system with adaptive competency to slow-varying behaviors. Therefore, it is less sensitive to normal slow variations, which eases the excessive dependency of monitoring performance on updating and, thus, decreases the risk of false adaptation to process disturbances. Despite the simplicity of the proposed idea and algorithm, the performance it achieves in the case studies indicates that it is smart and competitive as a feasible solution to analyze and monitor the regular slow-varying characteristics.