In this paper we consider lim _(R-) B_R^(f,x_0), in one case that f_x_0 (t) is a ABMV function on [0, ∞], and in another case that f∈L_(m-1)~1(R~) and x^k/~kf∈BV(R) when |k| = m-1 and f(x) = 0 when |x -x_0|<δ f...In this paper we consider lim _(R-) B_R^(f,x_0), in one case that f_x_0 (t) is a ABMV function on [0, ∞], and in another case that f∈L_(m-1)~1(R~) and x^k/~kf∈BV(R) when |k| = m-1 and f(x) = 0 when |x -x_0|<δ for some δ>0. Our theormes improve the results of Pan Wenjie ([1]).展开更多
For complex industrial processes with multiple operational conditions, it is important to develop effective monitoring algorithms to ensure the safety of production processes. This paper proposes a novel monitoring st...For complex industrial processes with multiple operational conditions, it is important to develop effective monitoring algorithms to ensure the safety of production processes. This paper proposes a novel monitoring strategy based on fuzzy C-means. The high dimensional historical data are transferred to a low dimensional subspace spanned by locality preserving projection. Then the scores in the novel subspace are classified into several overlapped clusters, each representing an operational mode. The distance statistics of each cluster are integrated though the membership values into a novel BID (Bayesian inference distance) monitoring index. The efficiency and effectiveness of the proposed method are validated though the Tennessee Eastman benchmark process.展开更多
文摘In this paper we consider lim _(R-) B_R^(f,x_0), in one case that f_x_0 (t) is a ABMV function on [0, ∞], and in another case that f∈L_(m-1)~1(R~) and x^k/~kf∈BV(R) when |k| = m-1 and f(x) = 0 when |x -x_0|<δ for some δ>0. Our theormes improve the results of Pan Wenjie ([1]).
基金Supported by the National Natural Science Foundation of China (61074079)Shanghai Leading Academic Discipline Project (B054)
文摘For complex industrial processes with multiple operational conditions, it is important to develop effective monitoring algorithms to ensure the safety of production processes. This paper proposes a novel monitoring strategy based on fuzzy C-means. The high dimensional historical data are transferred to a low dimensional subspace spanned by locality preserving projection. Then the scores in the novel subspace are classified into several overlapped clusters, each representing an operational mode. The distance statistics of each cluster are integrated though the membership values into a novel BID (Bayesian inference distance) monitoring index. The efficiency and effectiveness of the proposed method are validated though the Tennessee Eastman benchmark process.
