Resilience index

Morari (Chemical Eng. Science, 1983, Vol. 38, p. 1881) developed a very useliil measure of this property. The Morari resiliency index (MRl) gives an indication of the inherent controllability of a process. It depends on the controlled and manipulated variables, but it does not depend on the pairing of these vari-... 

Select manipulated variables. Find the set of manipulated variables that gives the largest Morari resiliency index (MRI). 

The Morari resiliency index (MRI) discussed in Chap. 16 can be used to... 

In this section, general mathematical formulations and graphic interpretations are presented for several resilience analysis problems (1) feasibility test, (2) resilience (flexibility) test, (3) flexibility index, and (4) resilience index. 

A primary disadvantage of the flexibility index is the need to solve 2 (N)LPs corresponding to the vertex directions when the critical point must be a vertex of the hyperrectangle 0(F). To decrease the required computational effort, Saboo et al. (1985) define a different index, the resilience index (RI), to measure the size of feasible region R. 

Fig. 6. Resilience index (RI) defines largest polytope P for which HEN is resilient.

Example 5 (adapted from Grossmann and Floudas, 1987). The resilience index is to be calculated for the HEN shown in Fig. 4. The following series of LPs is formulated to determine the maximum load uncertainty allowed in a positive direction on each stream ... 

In order to compare the resilience index with the flexibility index, suppose that the RI is scaled in terms of temperature rather than load. Then the temperature RI is 6.67 K (Table III), limited by positive uncertainty in the supply temperature of stream 4. (Note that the limiting uncertainty direction changes when the RI is rescaled from load to temperature.) This means that the HEN can tolerate uncertainty of 6.67 K in any individual stream supply temperature in either a positive or negative direction. Because of linearity and convexity, it also means that the HEN can tolerate a total temperature uncertainty S,jTf - 7fN of 6.67 K, no matter how the uncertainty is distributed among the streams. Note that this does not mean that the HEN can tolerate uncertainties of 6.67 K in all... 

The preceding theorem describes an operability test for class 2 HENs. Similarly, by omitting the energy recovery constraint from flexibility index problem (15) or resilience index problem (19), an operability index could be defined for class 2 HENs. 

The resilience index, another measure of the largest uncertainties for which the HEN remains feasible, is the size of the largest total uncertainty load (polytope region) which the HEN can tolerate. 

The resilience index can be determined by maximizing the load uncertainty /, which the network can tolerate in either a positive or negative direction in each stream supply temperature. Then the resilience index is... 

RI Resilience index, kW (16) s Scale factor for family of hyperrectangles used to define the flexibility index, dimensionless (10) t Vector of temperatures T Temperature, K... 

Saboo, A. K., Morari, M. and Woodcock, D. C., Design of resilient processing plants— VIII. A resilience index for heat exchanger networks. Chem. Eng. Sci. 40, 1553 (1985). 

Minimum singular value is designated in some works by Morarl Resiliency Index. ... 

Solovyev, B.E., and D.R. Lewin, A Steady-state Process Resiliency Index for Non-linear Processes, Proc. DYCOPS 6, Jejudo Island, Korea (2001). 

Carvalho H (2013) An innovative agile and resilient index for the automotive supply chaitL Int J Agile Syst Manage 6(3) 258-278... 

After defining the sets of controlled and manipulated variables, steady state controllability indices like Niederlinski index, relative gain array, Morari resiliency index, condition number are determined (e.g. Luyben, 1990). The evaluation of the... 

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