Correlation dimension estimate and its potential use in analysis of gas-solid flows

Gas-solid flows are nonlinear systems. Therefore state-space analysis, a tool developed within the framework of nonlinear dynamics, could provide more useful insights into complex gas-solid flows. One of the positive aspects of state-space analysis is that the major properties of a system can be reproduced from the state-space trajectory (i.e., attractor) reconstructed from the time series of one single measured parameter. This method is widely used in gas-solid flows in fluidized beds. However, there exist different results in literature for correlation dimension (a key parameter to describe the reconstructed attractor) most of which might be underestimated. Incorrect estimates of correlation dimension could impede its use in the analysis of gas-solid flows. Here an often-neglected topic on dynamical correlation (a temporal concept), which could be the major cause for generally under-estimated correlation dimension (a spatial dimension), is highlighted and a solution is given. The technique is demonstrated by analyzing absolute pressure fluctuations from a cold fluidized bed. Comparison of estimated correlation dimensions based on the same pressure fluctuations indicates excluding dynamical correlation pairs does produce higher dimension estimates, just as expected.