The wavelet transform (WT) and the fractional Fourier transform (FRFT) are powerful tools for many applications in the field of signal processing. However, the signal analysis capability of the former is limited in the time-frequency plane. Although the latter has overcome such limitation and can provide signal representations in the fractional domain, it fails in obtaining local structures of the signal. In this paper, a novel fractional wavelet transform (FRWT) is proposed in order to rectify the limitations of the WT and the FRFT. The proposed transform not only inherits the advantages of multiresolution analysis of the WT, but also has the capability of signal representations in the fractional domain which is similar to the FRFT. Compared with the existing FRWT, the novel FRWT can offer signal representations in the time-fractional-frequency plane. Besides, it has explicit physical interpretation, low computational complexity and usefulness for practical applications. The validity of the theoretical derivations is demonstrated via simulations.

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This study considers the development of optimization models for grade transition of polyethylene solution polymerization processes. A detailed mathematical model is developed to capture the dynamics of the solution polymerization process. This includes time delay models for vapor and liquid recycle streams as well as a reduced, yet accurate, vapor-liquid equilibrium (VLE) model derived from rigorous VLE calculations. Simultaneous dynamic optimization approach is applied to solve the optimization problem to reduce off-spec production time and transition time. Two optimization formulations, single stage and multistage, are developed to deal with single-value target and specification bands of product properties, respectively. The results show significant reductions in grade transition time and off-spec production time. In addition, the multistage formulation designed for problems with specification bands outperforms its single stage counterpart. It minimizes transition time and off-spec production directly, and leads to higher performance control profiles.

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