An Intelligent Particle Filter With Adaptive M-H Resampling for Liquid-Level Estimation During Silicon Crystal Growth

Abstract

During the growth of silicon single crystals, it is critical to detect the liquid level of the silicon melt to ensure their high-quality production. Because noise statistics are difficult to determine in measured values of the liquid level, a particle filter (PF) with unknown statistics has been presented to estimate the liquid level. However, this approach leads to inaccurate results due to sample impoverishment. To alleviate this problem, we propose an intelligent PF method with an adaptive Metropolis–Hastings (M-H) resampling strategy. To accomplish this, we first design an M-H resampling strategy with two proposed distributions to resample low-weight particles. These distributions randomly select high-weight particles for the Gaussian mutations or high-weight and low-weight particles for crossover operations, so as to promote the movement of low-weight particles to high-probability regions. We also construct a self-adaptive function to further improve the overall particle quality, which is used to calculate the selection probability of these two proposed distributions according to the proportion of low-weight particles in all of the particles. Finally, the liquid level is estimated according to the particles after the modified resampling strategy is applied. A comparative evaluation of the proposed method with the adaptive genetic particle filter (AGPF) and the firefly algorithm intelligence optimized particle filter (FAIOPF) is conducted. Some results of the simulation and the practical experiment are presented; they indicate the proposed method offers accuracy improvements in the liquid-level estimation during the silicon crystal growth. More specifically, compared with the AGPF and the FAIOPF, the mean absolute error (MAE) of the proposed method has been reduced by approximately 53.3% and 99.5%, respectively.