Flotation Height Prediction under Stable and Vibration States in Air Cushion Furnace Based on Hard Division Method

Algorithm 1

	Input: geometric center points and , operation process training dataset  = {}, Line 1 represents ; is a time slice data presenting a point of Line 1. Time slice representing a vector includes all features at a fixed time.
	Output: stable state and vibration state.
	Step 1: The variables {, , , } are transformed into {, , , } utilizing SDAE.
	Determine the number of the intersection points of the curve Line 1 and curve ①, ②, ③. The starting point numbering of Line1 is set as . Along the trajectory direction of Line1, set intersection points numbering as (). The end point numbering of Line 1 is .
	Step 2: All time slices in interval [-] are set as cluster ; . is the mean value of all samples in , ; and is also the center of cluster .
	Step 3: For all clusters, any two clusters are merged, if the Euclidean distance between two centers of clusters is smaller than . The center of the merged cluster is recalculated.
	Step 4: Each sample in is compared to each centroid of each cluster and assigned to the cluster whose centroid is nearest. Update all of the cluster centers. Calculate the distance between the original cluster center and the updated cluster center. If the distance is less than a minimum clustering distance threshold ε, go to Step 5. Otherwise, return to Step 3 and  = , is the updated center of cluster .
	Step 5: The time discontinuous data in are sorted by time sequence and are divided into different subclusters. The different subclusters are described as , where .
	Step 6: For all , if dist (, ) < dist (, ), belongs to stable state; otherwise, belongs to vibration state.