Article pubs.acs.org/IECR
Online Fuzzy Assessment of Operating Performance and Cause Identification of Nonoptimal Grades for Industrial Processes Yan Liu,† Fuli Wang,†,‡ and Yuqing Chang*,†,‡ †
College of Information Science & Engineering, Northeastern University, 3 Lane 11, Wenhua Road, Heping District, Shenyang, Liaoning, 110819, China; ‡ State Key Laboratory of Integrated Automation of Process Industry Technology and Research Center of National Metallurgical Automation, Shenyang, Liaoning, 110819, China ABSTRACT: To pursue optimal comprehensive economic benefit, the process operating performance assessment on optimality becomes more and more critical for industrial processes. In this article, a novel method for online fuzzy assessment of the process operating performance and cause identification of nonoptimal performance grades is proposed. The contributions of this paper are summarized as follows: a new performance grade classification and identification method for modeling data is proposed; then, the assessment models for different performance grades are established through extracting the process variable correlation characteristics, which effectively avoids redundant information and provides the reference standards for online assessment ; in addition, besides the deterministic assessment results, such as optimal, suboptimal, etc., the performance grade conversion is also evaluated; when the process operating performance is nonoptimal, the responsible variables are identified based on the variable contributions. Finally, the feasibility and efficiency of the proposed method is illustrated with a case of gold hydrometallurgical process. as fuzzy assessment12,14,15 gray relational analysis (GRA),16 artificial neural networks (ANN),17 multivariate statistical method,18,19 etc. Among them, fuzzy assessment method is one of the most popular assessment methods,12,14,15 because it is consistent with the availability and uncertainty of information in our decision process as well as the vagueness of human feeling and recognition. However, in traditional fuzzy assessment, the determination of assessment index weights and the establishment of the membership functions usually strongly depend on human experiences, which reduces the practicality of the assessment method; moreover, the correlations between the process variables lead to information redundancy, which makes the assessment results inaccurate. The fundamental principle of GRA is to recognize the relevance degree among many factors according to the similarity level of the geometrical patterns of sequence curves. However, the existence of redundant information because of the correlations between the process variables also limits its applications. Recently, ANN has been applied to the assessment problems.13,17 The assessment model is established when using the ANN to describe the internal configuration between the inputs (process variables) and the outputs (historical known assessment results), and the new objects are evaluated based on this assessment model. To remove redundant information between the process variables, principal component analysis (PCA), one of the most widely used multivariate statistical methods, has been applied to the fields of controller performance assessment, product quality assessment and equipment performance assessment.18,19
1. INTRODUCTION Generally, complex industrial process has the characteristics of multiparameter, multiloop, large time-delay, strong coupling, and dynamic. Process operating performance could be affected by various factors, and unsatisfactory operation performance will result in poor economic benefit. Therefore, timely, accurate, and comprehensive grasping of the operation performance has very important practical significance in improving production efficiency and economic benefits, facilitating the production management, and making adjustments. In the past decades, lots of research works focusing on process monitoring have emerged.1−9 The purpose of process monitoring is to determine whether the process operating is normal or fault. However, to obtain higher quality products and greater economic benefits, only making the distinguish between normal and fault leaves much to be desired, and it should ensure the process operating performance as optimal as possible under normal operating conditions, which relates to the problem of process operating performance assessment on optimality. The purpose of process operating performance assessment on optimality is to determine the performance grade of the operation performance, such as optimal, suboptimal, general, poor, etc., under normal operating conditions, and different performance grades reflect different levels of the comprehensive economic benefit. Through evaluating, the managers and operators can understand process developments more clearly and develop proper strategy to adjust the process to the optimal operating performance. At present, the assessment problems mainly focus on the assessment of controller performance,10,11 equipment performance12 and product quality,13 etc., and many assessment methods according to above aspects have springed up, such © 2013 American Chemical Society
Received: Revised: Accepted: Published: 18022
July 14, 2013 October 25, 2013 November 22, 2013 November 22, 2013 dx.doi.org/10.1021/ie402243s | Ind. Eng. Chem. Res. 2013, 52, 18022−18030
Industrial & Engineering Chemistry Research
Article
data of different performance grades, and then the characteristics are defined as the standards for online assessment. In online assessment, the fuzzy memberships between online data window and each of the performance grade modeling data are calculated, and the process operating performance is evaluate based on a given assessment rule. One of possible assessment results is: (i) a certain performance grade; (ii) a performance grade conversion. When the process operating performance is nonoptimal, the contributions of the process variables to the fuzzy membership are defined and calculated for finding out the responsible variables. Finally, practical application and simulation clearly demonstrate the effectiveness and feasibility of the proposed method. The rest of this paper is organized as follows. First, a twostep performance grade classification and identification algorithm is proposed to separate modeling data representing different performance grades into different data sets and identify the performance grades correspondingly. Subsequently, the method of assessment model establishment and online fuzzy assessment are developed in Section 3 and the cause identification approach for nonoptimal performance grades is presented in Section 4. In Illustrations section, a case of a gold hydrometallurgical process is studied to demonstrate the feasibility and efficiency of the proposed method. Finally, the paper ends with some conclusions and acknowledgments.
However, in the traditional PCA-based assessment, it dose not define the standards for online comparison and assessment, and the physical meanings of assessment results are not demonstrated clearly. To the best of the authors’ knowledge, although many assessment methods have been proposed, only a little work has been published on the optimality assessment for industrial process operating performance. Recently, a probabilistic framework of online operating assessment for multimode industrial processes has been proposed,20 where an optimality index is defined and used to evaluate the process operating performance. However, the optimality index is constructed based on the optimized objective function, such as plant cost, profits, and product quality, which usually can not be obtained real-time in actual production, especially for the large scale complex industrial processes. Furthermore, only limited experience-based qualitative analysis is provided for nonoptimal performance grades and without a general method of quantitative analysis. The process operating performance referred to in this article is directly related with the comprehensive economic benefit. If the comprehensive economic benefit approaches or reaches the history optimal level, we believe that the process operating performance is optimal. According to the level of comprehensive economic benefit, the process operating performance can be divided into several different performance grades, which helps us to have an intuitive understanding on the process operation level. Generally speaking, comprehensive economic benefit is usually affected by many factors, such as raw materials fluctuation, process parameter drifts, changes of the external environment, process disturbance, and other uncertainties, and these changes are usually reflected in the change of process variable correlation characteristics. That is to say, the process variable correlation characteristics are different for different performance grades. Considering that: (i) it is not suitable for evaluating the process operating performance using the comprehensive economic benefit, because there is a large lag between the production and return; (ii) the process variable correlation characteristics contained in the online measurements reflect the process operating performance, we should fully explore and utilize these information in assessment. Conclusively, the process operating performance assessment involved in this study is to determine which performance grades the process belongs to basing on process variable correlation characteristics; when the operating performance is nonoptimal, the nonoptimal cause can be identified accurately. Therefore, accurately extracting the process variable correlation characteristic is very important for assessment. In a variety of characteristic extraction methods, PCA is one of the most popular methods on account of its good abilities in dimensionality reduction and decorrelation and will be adopted in this study. In this paper, an online fuzzy assessment of process operating performance and nonoptimal cause identification method is proposed. In order to identify the modeling data for different performance grades, a two-step performance grade classification and identification method for modeling data is proposed first of all. Then, based on the understanding that different performance grades contain different process variable correlation characteristics, the assessment models for each performance grade are established with PCA. Unlike the traditional PCAbased assessment, PCA used in our study is to extract the process variable correlation characteristics from the modeling
2. PERFORMANCE GRADE CLASSIFICATION AND IDENTIFICATION In process operating performance assessment, selecting the modeling data for each of performance grades from historical data is one of the most important prerequisites for establishing the assessment models. The purpose of performance grade classification and identification is to accurately classify the modeling data with different process variable correlation characteristics into different data sets and identify the performance grades for each data set. Generally speaking, the process operating performance usually remains at a certain performance grade over a longer period of time, especially for those satisfactory performance grades. But there is always performance grade conversion, and it is not at one stroke but gradually. Consider that the data corresponding to the performance grade conversion usually contain the characteristics of time-varying, dynamic, nonlinear, etc., which affect the accuracy of the assessment models, it is necessary to delete these data before modeling. In view of this, a two-step performance grade classification and identification algorithm based on modeling data is proposed. The first step is to classify the modeling data into different data sets according to the process variable correlation characteristics based on an improved subtractive clustering algorithm, and then each data set roughly represents a certain performance grade. Moreover, because each data set still mingles with data of performance grade conversions, the second step is to delete those data iteratively and identify the performance grades correspondingly. 2.1. Performance Grade Classification Based on Modeling Data. Although the process operating performance shows variability in long-term production process, the local correlation characteristics of the process variables will be very similar within the same performance grade, and different performance grades contain different process variable correlation characteristics. Therefore, the process variable correlation characteristics can be used for classifying. In addition, 18023
dx.doi.org/10.1021/ie402243s | Ind. Eng. Chem. Res. 2013, 52, 18022−18030
Industrial & Engineering Chemistry Research
Article
In view of this, classify each data window into a data set with the maximum similarity γk,c, and then obtain C data sets s1, s2, ..., sC. Each data set can roughly represent one performance grade. The loading matrices of data set sc are denoted as Pcic, ic = 1, 2, ..., Nc, where Nc is the number of data windows in sc. 2.2. Performance Grade Identification. In each data set, the loading matrices of the data windows belonging to a certain performance grade are relatively centralized, but those corresponding to performance grade conversions mainly disperse at the edge of the data set. Based on this understanding, we have reasons to only retain the data near the center of the data set. Here, an iterative method for deleting the performance grade conversion data is proposed. Then, performance grades for each data set are identified with some help of expert knowledge. The iterative procedures for data set sc are shown as follows
considering that a single sample can not characterize the process operating performance and is susceptible to noise, a data window with width H, (H ≥ 2J) is introduced as the basic analysis unit. Then modeling data X ∈ RN×J is cut into a series of data window X1, X2, ..., XK, where Xk = [x((k − 1)H + 1), ..., x(kH)]T ∈ RH×J, k = 1, 2, ..., K, and K = ⌊N/H⌋; the symbols N and J are the numbers of samples and process variables, respectively. In PCA, because the loading matrix is fully able to reveal the information of process variable correlations, the loading matrix Pk ∈ RJ×J of the data windows Xk are extracted and used for classifying. In a large number of clustering algorithms, subtractive clustering algorithm is very effective on account of its outstanding abilities in estimating the cluster number and cluster centers.21 To consider the different importance in different projection directions, we propose a weight loading matrix based subtractive clustering algorithm to achieve classification. For loading matrix Pk, the new density function is formulated as eq 1 K
ρk(1) =
⎡ ⎛
J
∑ exp⎢⎢−⎜⎜∑ i=1
⎣ ⎝ j=1
(1) Calculate the similarities γ(m) c,ic between the mean loading c,(m) c matrix P̅ and Pic using eq 3, where m is the iteration number, and the initial mean loading matrix is P̅c,(1) = P̅c. (2) Set a similarity threshold δ (0.5 < δ < 1). If the similarity between loading matrices Pcic and P̅c,(m) is smaller than δ, delete the data window corresponding to Pcic, and rename , ..., Pc,(m) the remaining loading matrices as Pc,(m) 1 Nc(m) , where (m) Nc is the number of the remaining loading matrices after the m th iteration, N(1) c = Nc . (3) Update the mean loading matrix using P 1c,(m) , ,...,Pc,(m) Pc,(m) 2 Nc(m) :
⎤ ωj(pk (j) − pi(j))T (pk (j) − pi(j)) ⎞⎥ ⎟ ,k ⎟⎥ αk2 ⎠⎦
(1)
= 1, 2, ..., K
ρ(1) k
where is the density value for loading matrix Pk, pk(j) is the j th column of Pk; set ρ̅1 as the maximum value of the densities: 1 ρ̅1 = max1≤k≤Kρ(1) k , and let P̅ be the first cluster center with 1 density value ρ̅ ; ωj = (1/j)/(∑hJ = 11/h), j = 1, 2, ..., J, is the weight to emphasize the importance of jth projection direction pk(j) and satisfies ∑j J= 1ωj = 1,0 < ···
