Designing with uncertainty

There are a number of general techniques suggested by the problem formulation. At the most detailed level of design, the design parameters need to be optimized in relation to performance criteria based on a nonlinear dynamic model. This points to a need for effective tools for dynamic optimization. At a more preliminary level in a hierarchy of techniques, it might be useful to evaluate steady-state performance or to carry out tests on achievable dynamic performance to eliminate infeasible options. Appropriate screening techniques are therefore needed. All these methods can use nominal models for initial analysis, but a full analysis should be based on design with uncertainty. 

The rest of this chapter is structured as follows. The next section considers general techniques for use in the integrated design approach proposed design with uncertainty, screening tools for disturbance rejection, and dynamic opti-... 

Some approaches to design with uncertainty are reviewed in order to identify the appropriate basic approach and relevant techniques from previous work. A new algorithm is then presented which builds on previous work and attempts to exploit the characteristics of the design problems. 

As noted by Grossmann et al. (1983), the problem of design with uncertainty is not well-defined and many different approaches exist. As discussed above, we are interested in solving problems in which the uncertainty is assumed to be defined by bounds on model characteristics or parameters and in which it is... 

The algorithm presented for design with uncertainty seems quite effective, but a number of useful extensions can be identified. 

Figure 2.5 Designing with uncertainty-the importance of durability.

As with any engineering design, the ET cover should be designed with safety factors because both design and construction introduce uncertainty regarding performance. Some safety factor concerns are similar between ET covers and conventional covers. However, control of water flow into the waste requires new safety factor considerations for the ET cover, including the following ... 

Since the student will build neither, and since the professor probably cannot answer certain questions because of secrecy agreements or lack of knowledge, the student must learn to live with uncertainty. He will also learn how to defend his own views, and how to present material so as to obtain a favorable response from others. These learning experiences, coupled with exposure to the process of design as distinct from that of analysis and synthesis, are the major purposes of an introductory design course. 

To provide designers with useful correlations by comparing such correlations with existing data and presenting correlation uncertainties whenever possible. 

GC-C-IRMS was first demonstrated by Matthews and Hayes (1978). However, it was somewhat later that Barrie and others (Barrie et al., 1984) coupled a GC, via a combustion interface, to a dual collector mass spectrometer to produce the forerunner of today s GC-C-IRMS instruments. Even so, true determinations of 815N values of individual compounds by GC-C-IRMS remained elusive until finally demonstrated by Hayes and co-workers (Merritt and Hayes, 1994). More recently the precision of GC-C-IRMS instruments has been improved further still with uncertainties in 813C values as small as 0.5 %o for samples containing 5 pmol C and 0.1 %o for 100 pmol samples having been demonstrated (Merritt and Hayes 1994). Instruments available commercially today, from several manufacturers, all conform to the same general principles of design. 

In situations where a drug is designed as a novel mechanism and the definitions of trial parameters are not well defined, the chances of failure are high. Exhibit 6.17 provides some insights into trial failures, showing that the road to clinical success is fraught with uncertainties. 

We require at least n equations to solve for n unknowns. In this example, we have five equations (7-20), but just three unknowns ([A], [B], [C]). The two extra equations allow us to estimate uncertainty in the unknowns. If you do more experiments, you will generally decrease the uncertainty in concentration. An efficient experimental design with five experiments leaves us with more uncertainty than if we had done nine experiments. However, we have cut our effort nearly in half with the efficient design. 

Nishida, N., Liu, Y.A. and Ichikawa, A., "Studies in Chemical Process Design and Synthesis II. Optimal Synthesis of Dynamic Process Systems with Uncertainty," AiChE J. Vol. 22, No. 3, pp 539-550, May 1976. 

To date, the use of semiinfinite methods in worst-case control system design with parametric uncertainty has been extremely limited because of the above... 

Fig, 3. Uncertainty in the nomenclature of various macroemulsion polymerization subdomains as a function of the nucleation mechanism and the average number of macroradicals per particle. The off-diagonal elements, designated with question marks, have properties of both emulsion and suspension polymerizations... 

---