Richard S.H. Mah

Nonlinear partial least squares

We propose a new nonparametric regression method for high-dimensional data, nonlinear partial least squares (NLPLS), which is motivated by projection-based regression methods, e.g. PLS, projection pursuit regression and feedforward neural networks. The model takes the form of a composition of two functions. The first function in the composition projects the predictor variables onto a lower-dimensional curve or surface yielding scores, and the second predicts the response variable from the scores. We implement NLPLS with feedforward neural networks. NLPLS often will produce a more parsimonious model (fewer score vectors) than projection-based methods. We extend the model to multiple response variables and discuss situations when multiple response variables should be modeled simultaneously and when they should be modeled with separate regressions. We provide empirical results that evaluate the performances of NLPLS, projection pursuit, and neural networks on response variable predictions and robustness to starting values.

Data Reconciliation and Gross Error Detection in Chemical Process Networks

Measurements made on stream flows in a chemical process network are expected to satisfy mass and energy balance equations in the steady state. Because of the presence of random and possibly gross errors, these balance equations are not generally satisfied. The problems of how to reconcile the measurements so that they satisfy the constraints and how to use the reconciled values to detect gross errors are considered in this article. Reconciliation of measurements is usually based on weighted least squares estimation under constraints, and detection of gross errors is based on the residuals obtained in the reconciliation step. The constraints resulting from the network structure introduce certain identifiability problems in gross error detection. A thorough review of such methodologies proposed in the chemical engineering literature is given, and those methodologies are illustrated by examples. A number of research problems of potential interest to statisticians are outlined.

Preliminary design of multiproduct noncontinuous plants using simulated annealing

Abstract A heuristic procedure using simulated annealing (SA) is developed for the preliminary design of multiproduct noncontinuous plants. The procedure determines equipment sizes/rates and allows structural features such as location of intermediate storage, in-phase and out-of-phase mode of operation and nonidentical parallel units in a stage. The procedure extends naturally to retrofit problems. An approach for choosing the best set of generic annealing parameters based on their parametric studies is described. The important issue of incorporation of design constraints in such an algorithm is also discussed. Several forms of simulated annealing algorithms are evaluated using illustrative problems, and results are compared with results from existing algorithms. The Metropolis algorithm for move acceptance with the Aarts and Van Laarhoven scheduling strategy performs the best and consistently gives solutions within 0.5% of the global optimum. This paper demonstrates the effectiveness of SA in solving complex problems of noncontinuous plant design.

OBSERVABILITY AND REDUNDANCY IN PROCESS DATA ESTIMATION

By analogy to the development for dynamic systems, concepts of observability and redundancy may be developed with respect to a steady state system. These concepts differ from their counterparts for dynamic systems in that they can be used to characterize individual variables and local behavior as well as system and global behavior. Relations between local observability, global observability, calculability and redundancy are established and explored in this paper. It is shown that these concepts are useful in characterizing the performance of process data estimators with regard to bias and uniqueness of an estimate, convergence of estimation procedures and the feasibility and implications of problem decomposition.

Effect of redundancy on estimation accuracy in process data reconciliation

Abstract For a steady-state process the accuracy of reconciled data may be measured by the trace of its covariance matrix of estimation errors. Quantitative relations are derived for the effects of adding and removing single measurements on estimation accuracy. It is proved that redundancy will never adversely affect estimation accuracy. It will always enhance estimation accuracy, if the measurements relate the process variables in a different way from the constraints. These relations are utilized to develop evolutionary strategies for selecting an optimal measurement structure.

MODELING LIQUID MASS TRANSFER IN HIGEE SEPARATION PROCESS

Correspondence concerning this paper should be addressed to Professor Richard S.H. Mah. Hsien-Hsin Tung is now affiliated with Department of Chemical Engineering, California Institute of Technology Penetration theory is used to describe the liquid mass transfer in Higee separation process. Within a possible range of effective areas, it is shown that the predicted mass transfer coefficients are in reasonable agreement with the estimated mass transfer coefficients. The estimated coefficients were calculated from the experimental data and the possible effective areas. Hence it is concluded the penetration theory is generally applicable to describe liquid mass transfer in Higee separation process. The comparison also suggests that liquid mixing at the junctions of packing materials may be more complete in Higee process than in traditional process.

Process trending with piecewise linear smoothing

Abstract Compression and trending are techniques widely used in the initial treatment of raw process data. Two popular methods, Box Car with Backward Slope and Swinging Door, were reviewed recently by Kennedy. In spite of their popularity, neither of these methods are designed to cope with process variability and outliers. They also require one or more parameters to be specified based on practical considerations. In this paper we propose a new method, Piecewise Linear Online Trending (PLOT), which is statistically based and which performs significantly better. Unlike the two existing methods, it adapts to process variability and noisy data, recognizes and eliminates outliers, and it is robust even in the presence of outliers. It fits the data better for the same number of trends. The fidelity of its performance may be fine-tuned with a single level of significance which may be set by the user without requiring any expertise in statistics. It may be used in an online or a batch mode, and interfaces easily with most existing packages.

An implicit enumeration scheme for the flowshop problem with no intermediate storage

Abstract The scheduling of batch processing of materials may be modeled as a flowshop scheduling problem with no intermediate storage, for which the objective is to minimize the makespan. This paper presents a branch and bound procedure which makes use of lower bounds based on estimates of the mean and the variance of makespans derived from the completion of fixed partial sequences of job assignments. Methods of obtaining these estimates are given and a heuristic rule is used to obtain an initial solution which serves as an upper bound to the optimum.

Observability and redundancy classification in process networks: Theorems and algorithms

Abstract The utility of observability and redundancy in characterizing the performance of process data estimators was established in previous studies [10]. In this paper two classification algorithms for determining local and global observability and redundancy for individual variables and measurements are presented. The concepts of biconnected components, perturbation subgraphs and feasible unmeasurable perturbations are introduced, and their properties are developed and used to effect classification, simplification and dimensional reduction. Step-by-step application of these algorithms is illustrated by examples.

Treatment of general steady state process models in gross error identification

Abstract Most statistical tests for identifying gross errors in steady state processes assume a simple model in which variables are directly measured and no unmeasured variables are present in the constraints. This note presents a procedure for transforming a general steady state model into the standard form required by these tests.