A New Partitioning Algorithm for Classification of Variables in Process Plant Monitoring

PONZONI, IGNACIO; SÁNCHEZ, MABEL C.; BRIGNOLE, NÉLIDA B.

Los Angeles, California, Estados Unidos

Conferencia; AIChE 1997 Annual Meeting; 1997

AIChE (American Institute for Chemical Engineering)

Scope The classification of the variables involved in plant model equations has proved to be a useful tool to solve instrumentation design or revamp problems. The classification of unmeasured variables, i.e. whether they are determinable or not, constitutes an interesting research topic. Although there are satisfactory procedures available for linear and bilinear systems, the methods employed for nonlinear systems present several drawbacks as regards flexibility or robustness. The first stage of this work was to review the existing equation-oriented techniques as ´well as those based on graph theory, which were implemented in order to assess their advantages and weaknesses. Since none of them was good enough, it was necessary to develop a new strategy, especially adapted to cope with the typical structures of monitoring system design matrices. The technique succeeds in finding the maximum number of blocks of minimum size in the plant occurrence matrix with relatively low computational expense. The core algorithm, whose purpose is the specification of subsets, is based on a depth-first search with heuristics through undirected graphs. The global strategy constitutes an interactive tool that guides the user to make decisions about the most convenient instrument configuration. The methodology involves an iterative refmement on the patterns. The partitioning yields an intermediate categorization far unmeasured variables and the expert user should detennine whether the pattern is acceptable. If not, he may decide, for example, to add or delete specific instruments, or to impose new constraints on the feasibility of the subsets. For testing purposes, the proposed procedure was applied to the instrumentation revamp of an existing industrial plant. It is interesting to nate that its range of applications is wide because it is not limited to instrumentation issues. For instance, the determination of the best partitioning and calculation order also helps the engineer to diagnose singularities and to identifY badly-posed problems at the modeling stage, thus making the choice of specifications easier. The Solution Strategy The method aims at performing a structural rearrangement of the occurrence matrix that involves the unmeasured variables, which is sparse and rectangular in shape. The global strategy drives an incremental search for assignment blocks of minimum order. Given the occurrence matrix, the method locates the 1 x 1 subsets by fonvard triangularization. For the location of 2x2 removable subsets, a modification of Stadtherr´s subroutine 2 (Stadtherr et aI, 1974) is proposed. In contrast with that algorithm, our search is recursive and builds the reordered matrix moving forward by rows instead of examining the original matrix backwards and forwards. We devised another procedure to fmd the 3x3 subsets. It is a modification of PLADAT´s strategy (Sanchez et aI, 1992), ´which has better robustness properties. Finally, we developed a new algoritlull called First Least-Connected Node (FLCN). It is the most appropriate for the detection of sets of order n = 4 or greater. The FLCN Algorithm implicitly associates an undirected graph to a predetermined submatrix obtained from the occurrence matrix. The method explores the graph by means of a depth-first search (DFS) in order to determine all the potential paths of length n-l. The computational expense of the FLCN Algorithm was evaluated by means of a recurrence formula in terms of the order of the subsets "n" and the average amount of adjacent nodes "p", which amounts to the degree of sparsity. In practice, "p" is approximately equal to the number of equations that contain a given variable. Therefore, its value does not increase significantly with the problem size. As to n, it also remains low because allowable subsets are usually small. Implementation Details At the first stage, the MA TLAB software for numeric computation was employed. Since it is an interpreter, it is ideal to develop prototypes in the study of experimental algorithms. Once the methods had been outlined, the code was translated to C language to enable handling huge matrices. The implementation uses memory resources efficiently thanks to the dynamic assignment of all its data structures. Besides, it is highly portable to machines with different sets of instructions and/or operating systems. The program was developed in a Pentium PC with a 133 Mhz processor clock rate under an MSDOS 6.2 operating system. To ensure the portability of the code, it was recompiled and run both in a Pentium machine under a LINUX operating system and in an ALPHA DEC 3000 MODEL 3001 AXP with a 150 Mhz processor clock rate under an OSFIl operating system.   Industrial Application The strategy was applied to the classification of unmeasured variables for the mass and energy balance equations of a real plant that separates ethane ITom natural gas. It has 87 units and 185 streams. The model consisted of 1069 equations and 1086 variables. The purpose ofthis study was to determine whether the existing instrumentation (297 measurements) yielded enough information to estimate the values of a set of unmeasured variables of interest. Since the information attainable with the original set of measurements resulted insufficient to get the desired level of process knowledge, the most convenient set of new instruments was selected with the help of this strategy. Conclusions and Future Work A new solution strategy to solve classification problems was developed. It manages to detect the maximum number of blocks in the occurrence matrix, overcoming some limitations of the already available techniques. The methodology turned out to be robust and efficient when applied to the set of model equations for an existing industrial plant of medium size. In view of the significant amount of complex decision-making required to solve classification problems, it would be worthwhile developing a decision support system (DSS) on the basis ofthese results, including automatic-diagnosis tools so as to aid engineers choose the best set of measurements. References Sanchez M.C., AJ. Bandoni and J.A. Romagnoli. "PLADAT: A Package for Process Variable Classification and Plant Data Reconciliation." Compo Chem. Eng., pp. S499-S506, 1992. Stadtherr M.A., W.A. Gifford and L.E. Scriven. "Efficient Solution of Sparse Sets of Design Equations." Chem. Eng. Sci., Vol. 29, No 4, pp. 1025-1034, 1974.