Time-Series Analysis Technologies Applied to the Study of Carbon Element Distribution Along Casting Direction in Continuous-Casting Billet

The carbon element distributions along casting direction at centerline position, V-shaped segregation band, and columnar to equiaxed transformation (CET) position in continuous-casting billet have been first obtained by the original position statistic distribution analysis (OPA). Different location points at a certain position were formed along the opposite direction of casting direction with the lapse of the time, so the carbon mass fractions of different location points at a certain position can be considered as a time series. Based on the actual result, some typical time-series analysis technologies, such as the autoregressive integrated moving average (ARIMA) model, were used to analyze the characteristics of the three time series. It is found that there is some periodicity in the carbon element distribution at centerline position, and the correlation relationship between centerline position and CET position is closer than that between the centerline position and V-shaped segregation band at the same location point along the casting direction. Moreover, the element distribution along the casting direction is one of the solidifying results with the lapse of the time, so it is possible to investigate the characteristics of the system about the solidification process of continuous-casting billet by using these time series. Then it shows that there is a chaos feature in the system about the solidification process of studied continuous-casting billet on the basis of Hurst exponents and saturated correlative dimensions. Meanwhile, the formation process of carbon element distribution along casting direction can be described as fractional Brownian motion, and the upper and lower limits of the number of internal independent variables were determined in order to describe the formation process of carbon element distributions at different positions of the studied billet. Finally, the stochastic extent at V-shaped segregation band is found to be the largest, and it needs more independent variables to describe its formation process than the other two positions.