Model-robust parameter design

Model-robust orthogonal designs Model-robust parameter designs Addelman A Sun h ... 

Robust parameter designs are used to identify the factor levels that reduce the variability of a process or product (Taguchi, 1987). In such experiments, the dispersion effects, which can be identified by examination of control-by-noise interactions (see Chapter 2), are particularly important and hence the models of primary interest are those that contain at least one control-by-noise interaction. This motivated Bingham and Li (2002) to introduce a model ordering in which models are ranked by their order of importance as follows. 

Addelman, S. (1962). Symmetrical and asymmetrical fractional factorial plans. Technometrics, 4, 47-58. Allen, T. T. and Bemshteyn, M. (2003). Supersaturated designs that maximize the probability of identifying active factors. Technometrics, 45, 92-97. Bingham, D. and Li, W. (2002). A class of optimal robust parameter designs. Journal of Quality Technology, 34, 244—259. Biswas, A. and Chaudhuri, P. (2002). An efficient design for model discrimination and ... 

Model validation is a process that involves establishing the predictive power of a model during the study design as well as in the data analysis stages. The predictive power is estimated through simulation that considers distributions of PK, PD, and study-design variables. A robust study design will provide accurate and precise model-parameter estimations that are insensitive to model assumptions. 

This chapter addresses the planning, design and optimization of a network of petrochemical processes under uncertainty and robust considerations. Similar to the previous chapter, robustness is analyzed based on both model robustness and solution robustness. Parameter uncertainty includes process yield, raw material and product prices, and lower product market demand. The expected value of perfect information (EVPI) and the value of the stochastic solution (VSS) are also investigated to illustrate numerically the value of including the randomness of the different model parameters. 

In practice decision makers typically are risk averse and the expected value approach does not take into account the variability of the solutions obtained under the probability distributions or scenarios considered for the uncertain parameters. Rosenhead et al. (1972) introduced the aspect of robustness as a criterion for strategic planning to address this issue. Building on the notion of robustness, Mulvey et al. (1995) developed the concept of robust optimization distinguishing between two different types of robust models. A model is solution robust if the solution obtained remains close to optimality for any realization of the uncertain parameters. The model itself is robust if it remains (almost) feasible for any realization of the uncertain parameters (model robust).36 Here, only solution robustness is of interest as the most important elements of uncertainty in production network design, namely demand volumes, costs, prices and exchange rates, should not lead to infeasibility problems under different scenarios considered. 

The MPC control problem illustrated in Eqs. (8-66) to (8-71) contains a variety of design parameters model horizon N, prediction horizon p, control horizon m, weighting factors Wj, move suppression factor 6, the constraint limits Bj, Q, and Dj, and the sampling period At. Some of these parameters can be used to tune the MPC strategy, notably the move suppression faclor 6, but details remain largely proprietary. One commercial controller, Honeywell s RMPCT (Robust Multivariable Predictive Control Technology), provides default tuning parameters based on the dynamic process model and the model uncertainty. 

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