Proceedings of the American Control Conference Arlington, VA June 25-27, 2001 Two-step Method for Gross Error Detection in Process Data Jian Chen Zheng Chen* Hongye Su Jian Chu National Laboratory of Industrial Control Technology, Institute of Advanced Process Control *Department of System Science and Engineering Zhejiang University Hangzhou 310027 R R. China E-mail: jchen76@163.com or jchen_@netease.com Abstract Three types of gross errors~measuremem biases, process leaks, and abnormal variances--are discussed. A new class of test statistics for gross error detection--the two-step method is proposed. This method includes two steps. The first step is to detect and eliminate abnormal variances in measured variables. The second step is to detect measurement biases and process leaks. In the second step, a mean-value transformation is introduced to improve the performance of gross error detection. Simulations are performed, and the two-step method is compared to the existing test statistics. It is shown that the new tests have superior overall performance, and can detect all three types of gross errors discussed in this paper, even gross errors of small magnitudes. Also the two-step method can easily distinguish measurement biases and process leaks from abnormal variances. 1. Introduction Process data inevitably have two types of errors: random errors which are usually supposed to be normally distributed with zero mean, and gross errors which are caused by measurement biases, process leaks, process disturbances, and malfunctioning instruments. The effect of random errors can be reduced by data reconciliation, while gross errors have bad effect on data reconciliation. So gross errors must be identified and eliminated before data reconciliation. Several statistical tests have been presented to detect gross errors, such as the univariate measurement test proposed by Mah and Tamhane (1982) tll, the maximum power test proposed by Almasy and Sztano (1975) t21, and the principal component test proposed by Tong and Crowe (1994) t31E41. The main drawback of these test statistics is that they can not detect all kinds of gross errors, especially for abnormal variances. Also they can not differentiate between various types of gross errors. 2. Gross error models The steady state process measurement model with measurement biases can be described as following: X--X* +6+C (1) s ~ N (0,E) where x = (p × 1) the vector of measured variables x* - (p X 1) the vector of the true value of measured variables 6 = (p × l) the vector of measurement biases 6 = (p X 1) the vector of random errors E = (p Xp) the variance-covariance matrix p = the number of measured variables The steady state process model with process leaks can be modeled by: Ax-yE:O (2) where A = (q Xp) the balance matrix y=diag[yl, Y2,. ...... Yq] 7~= the mass flow leak in process unit (node) i E= [1, 1.... ,1] T is a q × 1 vector q = the number of process units (nodes) Here, unmeasured variables are not considered because the process with unmeasured variables can be transformed to the process without unmeasured variables by combining some units. Additional to measurement biases and process leaks, there is another type of gross error--abnormal variances: The sample variances of measured variables are out of the normal range determined by the historical data. Abnormal variances include excessive normal 0-7803-6495-3/01/$10.00 © 2001 AACC 21 21